For most of the eighteenth century, electricity was a thing of sparks. Scientists rubbed glass globes, stored the charge in jars, and drew a crackle that lasted less than the blink of an eye. It was startling, but it was over almost before it began. Nobody could make electricity that simply kept going.
In Italy, Luigi Galvani had noticed something strange in the 1780s. A dead frog’s leg twitched when two different metals touched it. Galvani believed the electricity came from inside the animal. His countryman Alessandro Volta disagreed. He suspected the animal was only detecting the effect, and that the two different metals, with a moist material between them, were making it.
So Volta built a stack. He piled a disc of zinc, then a disc of silver, then a piece of cardboard soaked in salt water, and repeated that pattern again and again. When he touched wires to the two ends of the pile, he did not get a spark. He got something far stranger — a steady, continuous tingle that went on and on, as long as the wires stayed connected.
In 1800 he described his pile to the Royal Society in London. Electricity had stopped being a flash. It had become a flow. The first drawing of this chapter, Fig. 9.0-1, shows what he had built.
Q1. The wires of a torch are full of electrons even when the torch is switched off. So why does the bulb light up only at the moment you press the switch? Q2. A copper wire and a silk thread both feel solid and both can be tied in a knot. Why can charge travel along one of them and not the other? Q3. Two wires of the same metal and the same length are joined one after the other to the same cell, but one is thin and one is thick. Why would the thick one carry more current? Q4. Inside a wire the electrons drift from the negative terminal towards the positive terminal. Why, then, do we draw the current arrow pointing the other way? Q5. A torch cell is thrown away once it is finished, while a phone battery is charged and used again for years. What must be different about the chemical change inside the two?
9.1 Free Electrons And Electric Charge
Electricity is not something poured into a wire from outside. Everything a wire needs in order to carry a current is already inside it, sitting in its atoms. To understand a current, we must first look at what those atoms are made of.
9.1.1 Inside The Atom: Bound And Free Electrons
Every substance is made up of atoms. An atom is built from three smaller particles — electrons, protons and neutrons. The central part of the atom is called the nucleus, and it contains the protons and the neutrons. The electrons move around this nucleus in definite orbits, as shown in Fig. 9.1-1.
An electron carries a negative charge and a proton carries a positive charge, while a neutron carries no charge at all. The positive charge on a proton is exactly equal in magnitude to the negative charge on an electron. We write the charge on a proton as \(+e\) and the charge on an electron as \(-e\), where \(e\) is called the elementary charge, the smallest amount of charge that is found on its own in nature.
In a normal atom the number of electrons is equal to the number of protons. The positive and negative charges therefore cancel exactly, and the atom as a whole is electrically neutral.
Not every electron in an atom is held equally tightly. The electrons in the inner orbits lie close to the nucleus and are strongly attracted by it, and these are called bound electrons. The electrons in the outermost orbit are far from the nucleus and are only weakly attracted.
Because that attraction is weak, a small supply of energy is enough to pull an outermost electron away from its atom. Such detached electrons are called free electrons, and they can wander through the substance instead of staying with one atom.
Free Electrons The loosely held electrons of the outermost orbit, which can be detached from their atoms by a small supply of energy and can then move freely through the substance.
When an atom loses one or more electrons, it is left with more protons than electrons, so it becomes positively charged. When an atom gains one or more electrons, it becomes negatively charged. The flow of electric charge through a substance is nothing but the motion of its free electrons, and this is why free electrons are described as the charge carriers in a metal.
Bound electrons and free electrons are not different kinds of particle. Every electron is identical. The difference is only in how tightly the nucleus holds it — inner orbits are gripped strongly, the outermost orbit is gripped weakly and can be released.
9.1.2 Conductors, Semiconductors And Insulators
Substances differ enormously in how many free electrons they contain, and that single difference decides whether electricity can pass through them. The three groups are compared in Table 9.1, and Fig. 9.1-2 shows why they behave so differently.
Conductors are substances that contain a very large number of free electrons, so electric conduction through them is easy. Metals such as silver, copper and aluminium are good conductors. When electric charge is given to a conductor, it does not stay where it was placed — it spreads quickly over the entire outer surface of the conductor. The Earth, the human body, mercury and acidulated water are conductors too.
Semiconductors are substances such as silicon and germanium, which contain only a moderate number of free electrons. They therefore conduct electricity to a limited extent, far less freely than a metal does. Their number of free electrons, and hence their conductivity, can be increased by raising their temperature or by adding suitable impurities to them.
Insulators are substances such as wood, glass and rubber, which contain almost no free electrons. Electric conduction is not possible through them. If electric charge is given to an insulator, the charge simply stays at the point where it was placed and does not spread.
Table 9.1 — Conductors, Semiconductors And Insulators Compared
| Number of free electrons |
Very large |
Moderate |
Almost negligible |
| Conduction of electricity |
Takes place easily |
Takes place to a limited extent |
Does not take place |
| Charge given to it |
Spreads over the entire outer surface |
Spreads only partly |
Stays at the point where it is placed |
| Effect of raising temperature |
Conduction becomes more difficult |
Conduction becomes easier |
Remains an insulator |
| Examples |
Silver, copper, aluminium, mercury, acidulated water, human body |
Silicon, germanium |
Wood, glass, rubber |
Q2. A copper wire and a silk thread both feel solid and both can be tied in a knot. Why can charge travel along one of them and not the other?
A. Being solid has nothing to do with it. Copper is a metal and carries a huge number of free electrons, so charge given to it moves at once. Silk is an insulator with almost no free electrons, so charge placed on it has nothing to travel with and stays put.
9.1.3 Superconductors
Some materials behave in an extraordinary way when they are made very cold. At ordinary temperatures they conduct like other metals, but when they are cooled below a certain temperature, called the critical temperature, their behaviour changes completely.
Below that temperature they conduct electricity without offering any resistance at all, so a current flows through them without any loss of energy. This state is called superconductivity, and materials that show it are called superconductors. Mercury, lead, niobium and tin are examples.
A hospital MRI scanner needs an intensely strong and perfectly steady magnetic field, which an ordinary copper coil could not supply without overheating. Its magnet is therefore wound from a niobium–titanium superconducting wire and cooled with liquid helium. Once the current is started in the closed superconducting loop, it keeps circulating with no energy loss, holding the field steady for years without a battery being connected. This is why the scanner room must be kept cold, and why the loud knocking a patient hears comes from other coils, not from this one.
9.1.4 Electric Charge And Its Unit
In earlier classes you learnt that when two bodies are rubbed together, electrons are transferred from one body to the other. The body that gains electrons becomes negatively charged and the body that loses electrons becomes positively charged.
Notice that the two bodies always end up with charges that are equal in magnitude but opposite in nature, because every electron lost by one is exactly the electron gained by the other. This property of a body, which decides how it pushes or pulls other charged bodies, is called its electric charge. Like charges repel each other, while unlike charges attract each other.
The charge on a body is denoted by the symbol \(q\) or \(Q\). Its SI unit is the coulomb, written with the symbol C.
Charge \(q\) or \(Q\), SI unit coulomb (C). A positive sign means the body has lost electrons; a negative sign means it has gained them. The sign is not decoration — it tells you which way the body will push another charge.
Smaller Units Of Charge
A coulomb is a large amount of charge, so laboratory quantities are usually stated in smaller units — the millicoulomb (mC), the microcoulomb (µC) and the nanocoulomb (nC):
\[1\\ \\text{mC} = 10^{-3}\\ \\text{C},\\qquad 1\\ \\mu\\text{C} = 10^{-6}\\ \\text{C},\\qquad 1\\ \\text{nC} = 10^{-9}\\ \\text{C}\]
Before any charge is put into a formula, it must first be converted into coulomb, because the coulomb is the SI unit.
Blow up a balloon and rub it briskly on a woollen sleeve, then turn a tap on until a thin, steady thread of water runs. Hold the rubbed side of the balloon close to the water without touching it, and watch the stream bend towards the balloon. Rubbing has moved electrons onto the balloon.
9.1.5 The Quantum Nature Of Charge
A body becomes charged only by losing or gaining electrons, and electrons come in whole numbers. You cannot remove half an electron from an atom. So the charge on a body must always be a whole number of electronic charges, never anything in between.
This is what is meant by the quantum nature of charge. Stated in symbols, the charge on a body is
\[q = \\pm ne\]
where \(q\) is the charge on the body in coulomb (C), \(n\) is a whole number (\(n = 1, 2, 3, 4, \\ldots\)), and \(e\) is the charge on an electron, \(e = 1.6 \\times 10^{-19}\\ \\text{C}\). The plus sign is used for a body that has lost electrons and the minus sign for a body that has gained them.
The Quantum Nature Of Charge Electric charge always exists as an integral multiple of the electronic charge \(e\), so that \(q = \\pm ne\), where \(n\) is a whole number and \(e = 1.6 \\times 10^{-19}\\ \\text{C}\).
The charge on a body can therefore be \(\\pm e\), \(\\pm 2e\), \(\\pm 3e\), and so on. It can never be a fraction of \(e\), such as \(1.5e\) or \(0.9e\), because that would mean a fraction of an electron had been transferred.
Counting The Electrons On A Charged Body
1. Given: charge on the body \(q = -3.2\\ \\text{nC}\); charge on one electron \(e = 1.6 \\times 10^{-19}\\ \\text{C}\). To find: the number of electrons \(n\) gained by the body. First convert to SI: \(q = -3.2 \\times 10^{-9}\\ \\text{C}\), since \(1\\ \\text{nC} = 10^{-9}\\ \\text{C}\).
Relation used: \(q = \\pm ne\), rearranged to make \(n\) the subject, \(n = \\dfrac{|q|}{e}\). This is the right relation because the body was charged by transferring whole electrons, and the minus sign only tells us electrons were gained, not lost.
Substituting, \(n = \\dfrac{3.2 \\times 10^{-9}\\ \\text{C}}{1.6 \\times 10^{-19}\\ \\text{C}} = 2.0 \\times 10^{10}\). The unit coulomb cancels above and below, as it must, because a count of electrons has no unit.
The body has gained \(2 \\times 10^{10}\) electrons. The answer is a whole number, as the quantum nature of charge requires, and a body rubbed by hand transferring a few tens of thousands of millions of electrons is an entirely ordinary result.
9.2 Direction Of Flow Of Charge
We now know that a metal holds a great many free electrons. The next question is a natural one — if two pieces of metal are joined, which way do those free electrons travel, and what makes them stop?
9.2.1 Flow Of Electrons Between Two Conductors
Suppose two charged conductors are joined by a metallic wire, or are simply placed in contact. Free electrons then flow from the conductor having a higher concentration of electrons to the conductor having a lower concentration of electrons.
By concentration we mean how crowded the electrons are — how many of them there are for a given size of conductor. The flow does not go on for ever. The movement of electrons stops as soon as the concentration of electrons in both conductors has become equal.
Three cases make this clear, and it is worth working through all of them, because each one is a situation you will meet again later in the chapter.
Case 1: A Positively Charged Conductor Joined To An Uncharged One
In Fig. 9.2-1, a positively charged conductor \(A\) is joined by a metal wire to an uncharged conductor \(B\). Conductor \(A\) is short of electrons, so its electron concentration is lower than that of \(B\).
Electrons therefore move from the uncharged conductor \(B\) to the charged conductor \(A\), making up the deficit in \(A\). This movement continues until both conductors have an equal concentration of electrons.
Case 2: A Negatively Charged Conductor Joined To An Uncharged One
In Fig. 9.2-2, a negatively charged conductor \(A\) is joined by a metal wire to an uncharged conductor \(B\). This time \(A\) has an excess of electrons and \(B\) is neutral, so the concentration in \(A\) is the higher one.
Electrons therefore flow from \(A\) to \(B\). The movement stops when both conductors have acquired an equal concentration of electrons.
Case 3: A Negatively Charged Conductor Joined To A Positively Charged One
In Fig. 9.2-3, conductor \(A\) is negatively charged and conductor \(B\) is positively charged, and the two are joined by a metal wire. Conductor \(A\) has an excess of electrons while conductor \(B\) has a deficit of them, so the difference in concentration is now at its largest.
Electrons flow from \(A\) to \(B\), and again the flow continues until there is an equal concentration of electrons in both conductors.
The Earth is such an enormous conductor that adding or removing electrons barely changes its concentration. So a charged body joined to the Earth by a metal wire always loses its charge completely. This is what earthing means, and it is why a metal water pipe can quietly drain the charge from your body.
Which Way Will The Electrons Go?
1. Given: two identical metal spheres \(P\) and \(Q\) of the same size; \(P\) carries a charge of \(-6\\ \\text{nC}\) and \(Q\) carries a charge of \(-2\\ \\text{nC}\). They are joined by a copper wire. To find: the direction in which electrons flow, and when the flow stops.
Relation used: electrons flow from the conductor of higher electron concentration to the conductor of lower electron concentration. This applies here because both spheres are the same size, so a larger negative charge does mean a more crowded set of electrons.
Sphere \(P\) has \(-6\\ \\text{nC}\) and sphere \(Q\) has \(-2\\ \\text{nC}\). Both are negative, but \(P\) carries the greater excess of electrons, so \(P\) is the more crowded of the two.
Electrons flow through the wire from \(P\) to \(Q\), and stop when each sphere carries \(-4\\ \\text{nC}\), since the total charge of \(-8\\ \\text{nC}\) is then shared equally between two identical spheres. This is sensible — no charge has been created or destroyed, only shared.
Rub a plastic scale on a dry woollen cloth and check that it lifts small torn bits of paper. Now grip the rubbed surface firmly in your bare hand for a few seconds and test it again. It will lift nothing. Your body is a conductor, and the charge has flowed away through it.
9.2.2 The Electric Cell As A Source Of Electrons
All three cases above share one disappointing feature. The flow of electrons lasts only for a moment, because the two conductors quickly reach equal concentration and everything stops.
From this we can draw an important inference. The flow of electrons between two conductors joined by a metal wire can be maintained for a long time only if we can somehow keep an excess of electrons in one conductor and a deficit of electrons in the other. Something must keep restoring the difference as fast as the wire removes it.
This is exactly what an electric cell does. Inside a cell, a chemical reaction keeps an excess of electrons on one electrode and a deficit of electrons on the other electrode, and it goes on doing so for a sufficiently long time.
The electrode with the excess of electrons is the negative terminal of the cell, and the electrode with the deficit is the positive terminal. An electric cell therefore works as a source of electrons, and there is a continuous flow of electrons through the external circuit connected to it, from the negative terminal to the positive terminal. This chain is set out in FC 9.1.
Three identical metal spheres \(X\), \(Y\) and \(Z\) carry charges of \(+4\\ \\text{nC}\), \(0\) and \(-4\\ \\text{nC}\). Sphere \(X\) is joined to \(Y\) by a copper wire and then the wire is removed. State the direction of electron flow, and the charge left on each of \(X\) and \(Y\).
9.3 Electric Current As The Rate Of Flow Of Charge
A cell keeps charge moving through a wire, but so far we have only said that it moves. To do any physics we must be able to say how much moves, and how fast. That measurement is called the electric current.
9.3.1 Defining Electric Current
Think of a wire as a pipe and imagine slicing straight across it, at right angles to the length of the wire. Charge is streaming past that slice all the time the circuit is working, as shown in Fig. 9.3-1.
The more charge that crosses the slice each second, the stronger the flow. So the sensible way to measure the flow is to ask how much charge crosses that cross-section in one second. This quantity is called the electric current.
Electric Current Current is the rate of flow of charge across a cross-section normal to the direction of flow of current; it is measured in ampere (A).
If a charge \(Q\) flows through the cross-section of a conductor in a time \(t\), then the current is
\[\\text{Current }(I) = \\frac{\\text{charge }(Q)}{\\text{time }(t)}\]
where \(I\) is the current in ampere (A), \(Q\) is the charge that has crossed the section in coulomb (C), and \(t\) is the time taken in second (s). If the flow is not steady, this gives the average current over that time.
Current is a scalar quantity. Although we speak of the direction of a current, currents do not add like arrows in space; two currents meeting at a junction simply add up as numbers.
Charge and current are not the same thing. Charge is how much has flowed, measured in coulomb. Current is how fast it flows, measured in ampere, which is coulomb per second. A large charge passing slowly can give a small current.
9.3.3 The Ampere And Its Smaller Units
The unit of current follows directly from the relation \(I = \\dfrac{Q}{t}\), because dividing a charge by a time must divide their units in the same way:
\[\\text{unit of current} = \\frac{\\text{unit of charge}}{\\text{unit of time}}\]
The SI unit of charge is the coulomb and the SI unit of time is the second, so the SI unit of current is the coulomb per second. This unit is given the name ampere, and is denoted by the symbol A.
\[1\\ \\text{ampere (A)} = \\frac{1\\ \\text{coulomb (C)}}{1\\ \\text{second (s)}}\]
So the current in a conductor is \(1\\ \\text{A}\) when charge flows through it at the rate of one coulomb per second.
It is worth seeing how many electrons that is. One coulomb of charge is carried by
\[\\frac{1}{1.6 \\times 10^{-19}} = 6.25 \\times 10^{18}\\ \\text{electrons}\]
so if a current of \(1\\ \\text{A}\) flows through a conductor, it means that \(6.25 \\times 10^{18}\) electrons pass in one second across that cross-section of the conductor.
Many circuits carry currents far smaller than an ampere, and these are stated in the milliampere (mA) and the microampere (µA):
\[1\\ \\text{mA} = 10^{-3}\\ \\text{A},\\qquad 1\\ \\mu\\text{A} = 10^{-6}\\ \\text{A}\]
As always, a current given in mA or µA must be converted to ampere before it is put into a formula.
Finding A Small Current
1. Given: charge \(Q = 90\\ \\text{mC}\) passes through a cross-section of a conductor in time \(t = 30\\ \\text{s}\). To find: the current \(I\), in mA. Convert to SI first: \(Q = 90 \\times 10^{-3}\\ \\text{C} = 0.09\\ \\text{C}\).
Relation used: \(I = \\dfrac{Q}{t}\), the definition of current, which is all that is needed because both the charge and the time are given directly.
\(I = \\dfrac{0.09\\ \\text{C}}{30\\ \\text{s}} = 3 \\times 10^{-3}\\ \\text{A}\).
The current is \(3 \\times 10^{-3}\\ \\text{A}\), that is \(3\\ \\text{mA}\). A few milliampere is a very ordinary current for a small electronic circuit, so the size of the answer is reasonable.
A current of \(250\\ \\mu\\text{A}\) flows through a conductor for \(2\\ \\text{minutes}\). Find the charge that passes through it, and the number of electrons this represents. Take \(e = 1.6 \\times 10^{-19}\\ \\text{C}\).
9.4 Conventional And Electronic Flow Of Current
We have said that electrons flow from a crowded conductor to a less crowded one. Physics prefers to describe such flows by a quantity that decides the direction, rather than by counting crowds. Three familiar examples will show what such a quantity looks like.
9.4.1 Three Familiar Flows: Height, Water Level And Temperature
It is our common experience that a body released from a height always falls. In Fig. 9.4-1, the body moves from the higher level \(A\), away from the Earth, down to the lower level \(B\) near the Earth’s surface. In other words, it moves from a higher gravitational potential to a lower gravitational potential.
Water behaves in the same style. If two vessels containing water up to different levels are joined together by a tube, water flows out of vessel \(A\), which holds water up to a higher level, into vessel \(B\), which holds it up to a lower level. This is shown in Fig. 9.4-2. The flow happens because of the difference in hydrostatic pressure between the two vessels, and it continues until the level of water is the same in both.
Heat tells the same story. If two bodies at different temperatures are kept in contact, heat flows by conduction from body \(A\) at the higher temperature to body \(B\) at the lower temperature, as in Fig. 9.4-3. The flow continues until both bodies have acquired the same temperature.
In each case one quantity — height, water level, temperature — decides which way the flow goes, and the flow stops when that quantity becomes equal on the two sides. Table 9.3 sets the three alongside the electrical case we are about to meet.
Table 9.3 — Four Flows And What Decides Their Direction
| Falling body |
The body |
Gravitational potential (height) |
It reaches the lowest available level |
| Two joined vessels |
Water |
Hydrostatic pressure (water level) |
The levels become equal |
| Two bodies in contact |
Heat |
Temperature |
The temperatures become equal |
| Two joined conductors |
Electrons |
Electric potential |
The potentials become equal |
9.4.2 Electric Potential Of A Conductor
In just the same manner, when two charged conductors are joined by a metal wire, the direction in which the electrons flow is decided by a quantity called the electric potential of the conductor. It is the electrical equivalent of height, or of water level, or of temperature.
The rule connecting potential to electrons is short, and it is worth learning exactly. A conductor having an excess of electrons is said to be at a negative, or lower, potential. A conductor having a deficit of electrons is said to be at a positive, or higher, potential.
That may look upside down at first, and it is worth seeing why it is not. Potential is defined by what happens to positive charge, and a positive charge is pushed away from a conductor that is short of electrons. So a conductor short of electrons is the high one, even though electrons themselves travel towards it.
9.4.3 Why Conventional Current Opposes Electron Flow
Fig. 9.4-4 puts the pieces together. A positively charged conductor \(A\), having a deficit of electrons and therefore at a high potential, is joined by a metal wire to a negatively charged conductor \(B\), having an excess of electrons and therefore at a low potential.
Electrons flow through the wire from \(B\) to \(A\) — that is, from the low potential to the high potential. The rate of flow of electrons in a direction is called the electronic current in that direction.
Now recall the pattern of the three earlier examples. Bodies fall from a high level to a low level, water runs from a high level to a low level, heat passes from a high temperature to a low temperature. To keep electricity in step with that pattern, we say that the electric current flows from a body at higher potential to a body at lower potential — which is the direction opposite to the flow of electrons.
Conventionally, then, the direction of current is taken as positive in the direction in which positive charge flows. Since electrons are negative, a flow of electrons in some direction counts as a current in the opposite direction. This current is the conventional current, and it is what we mean from now on when we simply say ‘the current’.
The magnitude of the conventional current is the rate of flow of total charge across the given cross-section. Only its direction, not its size, differs from the electronic current.
This also settles the question left open in the previous section. In an electrolyte, positive ions drifting one way and negative ions drifting the other way both count as conventional current in the same direction, which is why their contributions add instead of cancelling.
Electronic current and conventional current describe the same flow. The electronic current points the way the electrons actually drift. The conventional current points the opposite way, from high potential to low potential. Circuit diagrams always mark the conventional current, so that is the arrow you draw.
Q4. Inside a wire the electrons drift from the negative terminal towards the positive terminal. Why, then, do we draw the current arrow pointing the other way?
A. Because current is defined by the flow of positive charge, so that electricity follows the same pattern as falling bodies, water and heat — always from high to low. Electrons are negative, so their drift counts as a current the other way.
This convention was fixed long before anyone knew electrons existed. Benjamin Franklin chose which kind of charge to call positive in the 1750s, and J. J. Thomson identified the electron only in 1897. By then circuits and instruments everywhere were built around the older choice, so it was kept.
Reading The Two Directions From The Charges
1. Given: two conductors \(M\) and \(N\) are joined by a copper wire; \(M\) has a deficit of electrons and \(N\) has an excess of electrons. To find: (a) which conductor is at the higher potential, (b) the direction of flow of electrons, and (c) the direction of the conventional current.
Rules used: a conductor with a deficit of electrons is at a higher, positive potential and one with an excess is at a lower, negative potential; electrons flow from lower to higher potential; conventional current is opposite to the flow of electrons. No formula is needed, because only directions are asked for.
\(M\) has a deficit, so \(M\) is at the higher potential and \(N\) is at the lower potential. Electrons therefore travel through the wire from \(N\) to \(M\). The conventional current, being opposite to this, travels from \(M\) to \(N\).
So \(M\) is at the higher potential, the electrons flow from \(N\) to \(M\), and the current flows from \(M\) to \(N\). The check is that the current runs from high potential to low potential, exactly as water runs from a high level to a low one.
A conductor \(PQ\) is joined to a cell so that end \(P\) is at a low potential and end \(Q\) is at a high potential. State, with a reason in each case, (a) which end has the excess of electrons, (b) the direction of flow of electrons inside \(PQ\), and (c) the direction of the conventional current inside \(PQ\).
9.5 Work Done In Transferring Charge And Potential Difference
Electric potential has so far been a word for whichever conductor is ‘higher’. That is not enough for physics, because we cannot measure a word. In this section we turn potential into a quantity, by asking what it costs to move charge about.
9.5.1 Electric Potential At A Point
We know that like charges repel and unlike charges attract. So if we want to build up an excess or a deficit of electrons at some point, we cannot do it for nothing. Charges already there push back, and some work has to be done in moving the charges against those forces.
To measure that work we need a sensible starting place, and there is one. The force between two charges becomes zero when they are infinitely far apart. A point at infinity is therefore the natural ‘nowhere’ from which to begin, because no electric force acts there. This is why the potential at a point is measured by the work done in bringing a charge from infinity up to that point, as shown in Fig. 9.5-1.
If work \(W'\) is done in bringing a charge \(q\) from infinity to a point, then the potential at that point is
\[V = \\frac{W'}{q}\]
where \(V\) is the potential at the point in volt (V), \(W'\) is the work done in joule (J), and \(q\) is the charge brought in from infinity in coulomb (C). Dividing by \(q\) matters — it makes the answer a property of the point itself, not of the particular charge we happened to carry there.
Potential is a scalar quantity. Its SI unit is the joule per coulomb, which is given the name volt and the symbol V.
9.5.2 Potential Difference Between Two Points
In practice we almost never need the potential at a single point. What a circuit responds to is the difference in potential between two places, just as water responds to a difference in level rather than to height above the sea.
So the potential difference between two conductors is measured in terms of the work done in transferring charge from one conductor to the other through a metallic wire. This is illustrated in Fig. 9.5-2.
Potential Difference The potential difference between two conductors is equal to the work done in transferring a unit positive charge from one conductor to the other conductor; it is measured in volt (V).
If work \(W\) is done in transferring a test charge \(q\) from one conductor to the other, then the potential difference between them is
\[V\_1 - V\_2 = \\frac{W}{q}\]
where \(V\_1\) and \(V\_2\) are the potentials of the two conductors in volt (V), \(W\) is the work done in joule (J), and \(q\) is the charge transferred in coulomb (C). Potential difference, like potential, is a scalar quantity.
Very often we want the work rather than the potential difference. Writing the potential difference simply as \(V\) and multiplying both sides by \(q\) rearranges the same relation into
\[W = q \\times V\]
so the work done in moving a charge \(q\) through a potential difference \(V\) is the charge multiplied by the potential difference, in joule.
Potential belongs to one point, measured from infinity. Potential difference belongs to a pair of points, and is the one a circuit actually uses. A cell is marked with a potential difference, never with a potential — just as a waterfall is described by its drop, not by its height above sea level.
9.5.3 The Volt
The unit of potential difference follows from the relation \(V = \\dfrac{W}{q}\), in the same way that the ampere followed from \(I = \\dfrac{Q}{t}\):
\[\\text{unit of potential difference} = \\frac{\\text{unit of work}}{\\text{unit of charge}}\]
The SI unit of work is the joule and the SI unit of charge is the coulomb, so potential difference is measured in joule per coulomb. This unit is named the volt and is written V.
\[1\\ \\text{volt} = \\frac{1\\ \\text{joule}}{1\\ \\text{coulomb}},\\qquad \\text{that is}\\qquad 1\\ \\text{V} = \\frac{1\\ \\text{J}}{1\\ \\text{C}}\]
Stating this in words gives the meaning of the unit, and it is worth being able to say it exactly. The potential difference between two points is said to be 1 volt if the work done in transferring 1 coulomb of charge from one point to the other point is 1 joule.
The ‘1.5 V’ printed on a torch cell is not telling you how strong it is, how long it will last, or how much current it can supply. It is telling you the energy each coulomb of charge is given as it passes through the cell — one and a half joule per coulomb. This is why four such cells joined end to end in a torch give 6 V: each coulomb now collects energy four times over on its way round. It is also why a 1.5 V cell is harmless to touch, while mains voltage, hundreds of times greater per coulomb, is not.
Work Needed To Move A Charge
1. Given: charge \(q = 5\\ \\text{C}\); potential difference \(V = 12\\ \\text{V}\). To find: the work \(W\) done in moving the charge through this potential difference. Both quantities are already in SI units, so no conversion is needed.
Relation used: \(V = \\dfrac{W}{q}\), rearranged to \(W = q \\times V\), because the work is the unknown and both the charge and the potential difference are given.
\(W = 5\\ \\text{C} \\times 12\\ \\text{V} = 60\\ \\text{J}\), since one coulomb multiplied by one volt is one joule, by the definition of the volt.
The work done is \(60\\ \\text{J}\). The size is sensible — each coulomb costs \(12\\ \\text{J}\), and there are five of them.
Finding A Potential Difference From The Work Done
1. Given: charge transferred \(q = 400\\ \\text{mC}\); work done \(W = 1.8\\ \\text{J}\). To find: the potential difference \(V\) across the wire. Convert the charge to SI first: \(q = 400 \\times 10^{-3}\\ \\text{C} = 0.4\\ \\text{C}\).
Relation used: \(V = \\dfrac{W}{q}\), the definition of potential difference, since the work done and the charge transferred are both known.
\(V = \\dfrac{1.8\\ \\text{J}}{0.4\\ \\text{C}} = 4.5\\ \\text{V}\).
The potential difference across the wire is \(4.5\\ \\text{V}\). A joule divided by a coulomb is a volt, so the unit is right, and \(4.5\\ \\text{V}\) is the sort of value three small cells in a row would give.
A cell drives a charge of \(2\\ \\text{C}\) around a circuit and does \(18\\ \\text{J}\) of work on it. Find the potential difference across the cell. How much work would the same cell do on a charge of \(50\\ \\text{mC}\)?
9.6 Electrical Resistance
A cell provides the push, and the free electrons are there to be pushed. Yet a wire does not let charge through as freely as an open pipe lets water through. Every metallic wire fights the flow to some extent, and this section is about that opposition.
When current flows through a metallic wire, the wire offers some obstruction to it. That obstruction is called resistance.
Electrical Resistance The obstruction offered to the flow of current by a conductor is called its electrical resistance; it is measured in ohm (Ω).
9.6.1 The Cause Of Resistance
To see where the obstruction comes from, look at what the free electrons are actually doing. Fig. 9.6-1 shows the inside of a metal wire in two situations.
When no cell is connected across the wire, its free electrons move about inside the conductor in a completely random manner, as in Fig. 9.6-1 (a). They travel in all directions equally, so no charge is carried from one end of the wire to the other.
Now the ends of the wire are connected to a cell. The electrons begin moving from the negative terminal of the cell towards its positive terminal through the metal wire. But their journey is anything but smooth.
During their movement, the electrons collide with the fixed positive ions of the wire and with other free electrons. At each such collision their speed decreases and their direction of motion changes. After each collision they again accelerate towards the positive terminal, and then suffer fresh collisions with other positive ions and free electrons. The whole cycle is set out in FC 9.2.
Because this process repeats endlessly, the electrons never move in bulk with steadily increasing speed from one end of the wire to the other. Instead they drift slowly towards the positive terminal, edging forward between collisions. This constant interruption is how a wire offers resistance to the flow of electrons, and therefore to the current through it.
The rule linking current and potential difference is named after Georg Simon Ohm, a German schoolteacher who was measuring circuits in the 1820s with equipment he largely built himself. Working with wires of different lengths and thicknesses, he found that the current through a wire rose in exact step with the electrical push applied across it. He published this in 1827. The reception was cold — much of the German scientific establishment thought the work unimportant, and Ohm resigned his post in disappointment. It took nearly fifteen years for the result to be recognised, and the unit of resistance now carries his name.
9.6.2 Ohm’s Law
Suppose a current \(I\) flows through a wire when the potential difference across the ends of the wire is \(V\). The resistance offered by the wire to the flow of current is the ratio of the potential difference across it to the current flowing in it. In symbols,
\[R = \\frac{V}{I} \\qquad \\text{or} \\qquad V = IR\]
where \(V\) is the potential difference across the ends of the wire in volt (V), \(I\) is the current flowing in the wire in ampere (A), and \(R\) is the resistance of the wire in ohm (Ω). Resistance is a scalar quantity.
Behind this ratio lies the law itself, and the law carries a condition that must never be dropped.
Ohm’s Law The current flowing through a conductor is directly proportional to the potential difference applied across its ends, provided its temperature remains constant. That is, \(I \\propto V\), or \(V \\propto I\), or \(V = IR\), where \(R\) is the resistance of the conductor.
The condition is not a formality. A wire warms up when it carries current, and section 9.6.4 will show that a warmer wire has a greater resistance. Ohm’s law describes what a conductor does while its temperature is held steady.
Resistance \(R\), SI unit ohm, symbol Ω. Resistance is never negative — a conductor can only obstruct a current, never help it along. Before dividing, put \(V\) in volt and \(I\) in ampere; a current left in mA gives an answer a thousand times too large.
Ohm’s Law Seen As A Graph
Because \(V\) and \(I\) are directly proportional at constant temperature, plotting one against the other must give a straight line through the origin. That line is drawn in Fig. 9.6-2.
Fig. 9.6-2 — Potential Difference Against Current For A Metal Wire Start with the axes. The horizontal axis carries the current through the wire, measured in ampere (A). The vertical axis carries the potential difference across the same wire, measured in volt (V). Every plotted point is one pair of readings taken from the same wire at the same temperature. Next, the shape. The points lie on a straight line, so \(V\) and \(I\) rise in step: doubling the current from \(0.4\\ \\text{A}\) to \(0.8\\ \\text{A}\) doubles the potential difference from \(2.0\\ \\text{V}\) to \(4.0\\ \\text{V}\). That is exactly what direct proportionality means. Now the origin. The line passes through \((0, 0)\), which says that with no potential difference across the wire there is no current in it. A line that met the vertical axis above the origin would not obey Ohm’s law. Finally the gradient, which is where the physics is. The gradient is the increase in \(V\) divided by the matching increase in \(I\), read off the marked triangle: \(\\dfrac{2.0\\ \\text{V}}{0.4\\ \\text{A}} = 5\\ \\Omega\). Since \(R = \\dfrac{V}{I}\), the gradient of a \(V\)–\(I\) graph is the resistance of the wire, so this wire has a resistance of \(5\\ \\Omega\). A steeper line would mean a more resistant wire.
9.6.3 The Ohm
Once again the unit follows from the relation. From \(R = \\dfrac{V}{I}\),
\[\\text{unit of resistance} = \\frac{\\text{unit of potential difference}}{\\text{unit of current}}\]
The SI unit of potential difference is the volt and the SI unit of current is the ampere, so the SI unit of resistance is the volt per ampere. This unit is named the ohm and is written with the Greek letter Ω.
\[1\\ \\text{ohm} = \\frac{1\\ \\text{volt}}{1\\ \\text{ampere}},\\qquad \\text{that is}\\qquad 1\\ \\Omega = \\frac{1\\ \\text{V}}{1\\ \\text{A}}\]
In words: the resistance of a conductor is said to be 1 ohm if a current of 1 ampere flows through it when the potential difference across its ends is 1 volt.
Resistance Of A Bulb Filament
1. Given: potential difference across the filament \(V = 6\\ \\text{V}\); current through it \(I = 0.4\\ \\text{A}\). To find: the resistance \(R\) of the filament while it glows. Both values are already in SI units.
Relation used: \(R = \\dfrac{V}{I}\), since the potential difference across the filament and the current through it are both known and the filament is at a steady temperature while glowing.
\(R = \\dfrac{6\\ \\text{V}}{0.4\\ \\text{A}} = 15\\ \\Omega\), because a volt divided by an ampere is an ohm.
The resistance of the filament is \(15\\ \\Omega\). A small torch bulb drawing a few tenths of an ampere from a few volt does have a filament resistance of this order, so the answer is physically sensible.
Current Through A Wire, Given In Milliampere
1. Given: resistance of the wire \(R = 15\\ \\Omega\); potential difference across it \(V = 4.5\\ \\text{V}\). To find: the current \(I\) through the wire, in mA.
Relation used: Ohm’s law \(V = IR\), rearranged to make the current the subject, \(I = \\dfrac{V}{R}\). This is valid here because the wire is at constant temperature.
\(I = \\dfrac{4.5\\ \\text{V}}{15\\ \\Omega} = 0.3\\ \\text{A}\). Converting, \(0.3\\ \\text{A} = 0.3 \\times 10^{3}\\ \\text{mA} = 300\\ \\text{mA}\).
The current through the wire is \(0.3\\ \\text{A}\), that is \(300\\ \\text{mA}\). The check is easy — a smaller potential difference than in Example 9.8 across a larger resistance must give a smaller current, and it does.
9.6.4 Factors Affecting The Resistance Of A Conductor
Resistance is caused by collisions, so anything that changes the number of collisions an electron suffers will change the resistance. Four things do so, and they are drawn in Fig. 9.6-3.
(1) The material of the wire. The resistance of a wire depends on how many collisions the electrons moving through it suffer with the other electrons and the fixed positive ions. In different materials, the concentration of electrons and the arrangement of atoms are different. Therefore the resistance of wires of the same length and same area of cross-section, but of different materials, differs depending on their material. Good conductors, which have a higher concentration of free electrons, such as metals, offer less resistance.
(2) The length of the wire. The number of collisions suffered by the moving electrons will be more if they have to travel a longer distance in the wire. Therefore a long wire offers more resistance than a short wire — that is, the resistance of a wire is proportional to the length of the wire.
(3) The area of cross-section of the wire. In a thick wire, the electrons get a larger area of cross-section to flow through as compared with a thin wire. Therefore a thick wire offers less resistance — that is, the resistance of a wire is proportional to \(\\dfrac{1}{\\text{area of cross-section of the wire}}\).
(4) The temperature of the wire. If the temperature of a wire increases, the ions in it vibrate more violently. As a result the number of collisions increases, and hence the resistance of the wire increases. In short, the resistance of a wire increases with an increase in its temperature.
Q3. Two wires of the same metal and the same length are joined one after the other to the same cell, but one is thin and one is thick. Why would the thick one carry more current?
A. The thick wire gives the electrons a larger area of cross-section to move through, so they suffer fewer collisions and its resistance is smaller. With the same potential difference applied, \(I = V/R\) gives a larger current through the smaller resistance.
A wire of resistance \(8\\ \\Omega\) is stretched until it is twice as long, its material staying the same and its cross-section becoming correspondingly thinner. State, with reasons, whether its resistance increases or decreases, and whether the current drawn from a given cell rises or falls.
9.7 Sources Of Direct Current
Everything so far has assumed that something keeps the potential difference up. That something is a source of current, and the commonest one is the cell you drop into a torch.
9.7.1 Direct Current And The Electric Cell
We are all familiar with the cells used in a torch to light up its bulb. These cells are the source of direct current, abbreviated as d.c., which lights up the bulb. In the circuit of Fig. 9.7-1, the current flows from the positive terminal of the cell, through the bulb of the torch, to its negative terminal.
In a dry cell the two terminals are easy to identify. The brass cap projecting out at the centre acts as the positive terminal of the cell, and the base of the zinc case acts as the negative terminal.
The magnitude of the current given by a cell remains constant for a sufficiently long time. When the cell finally gets discharged, it stops giving current and becomes useless.
Direct Current Direct current (d.c.) is a current of constant magnitude flowing in one direction.
What Is Inside A Cell
In a cell, chemical energy changes into electrical energy when it sends a current in a circuit. The construction is simple in principle, and is shown in Fig. 9.7-2.
A cell basically consists of a vessel containing two conducting rods, called the electrodes, held at some separation and placed or immersed in a solution, or a jelly, called the electrolyte. The chemical action between the electrolyte and the electrodes is what maintains the excess of electrons at one electrode and the deficit at the other, as we saw in section 9.2.
A cell is a single unit with one pair of electrodes. A battery is two or more cells joined together to give a larger potential difference. The 1.5 V unit you buy for a torch is a cell; the 9 V block and the unit under a car bonnet are batteries.
Kinds Of Cells
Cells are of two kinds — primary cells, and secondary cells or accumulators.
9.7.2 Primary Cells
Primary cells provide current as a result of an irreversible chemical reaction. Once the entire chemical energy in them has been converted into electrical energy, the reaction cannot be run backwards, so the cells are simply discarded after use.
These are therefore ‘use and throw’ cells, and they cannot be recharged. Depending upon the material of the electrodes and of the electrolyte, we have different types of primary cells — the simple voltaic cell, the Leclanche cell, the Daniel cell and the dry cell.
9.7.3 Secondary Cells Or Accumulators
Secondary cells, also called accumulators, also provide current as a result of a chemical reaction. The difference is that in these cells the chemical reaction is reversible, and so they can be recharged after use.
After taking the electrolyte and the electrodes in a vessel, the cell is first charged by connecting it to a source of direct current. During charging, electrical energy changes into chemical energy and gets stored in the cell. When the cell is later used to send current in a circuit, that chemical energy changes back into electrical energy. FC 9.3 shows the two directions of this exchange.
Because they can be recharged again and again, these cells can be used over a very long period. The lead, or acid, accumulator and the Ni-Fe, or alkali, accumulator are the two types of secondary cell commonly used to provide low as well as high current.
A number of lead accumulator cells are used together as the battery in a car, because such a battery is capable of giving a high current. Low-current rechargeable cells are widely used in toys and mobile phones. Secondary cells are also called storage cells.
Table 9.4 — Primary Cell Compared With Secondary Cell
| Chemical reaction |
Irreversible |
Reversible |
| Energy conversion |
Chemical energy is converted into electrical energy when current is drawn from it |
Electrical energy converts into chemical energy when current is passed into it during charging, while chemical energy converts into electrical energy when current is drawn from it during discharging |
| Recharging |
It cannot be recharged |
It can be recharged |
| Internal resistance |
High |
Low |
| Current supplied |
Capable of giving a weak current only |
Can provide low as well as high current |
| Weight and cost |
Light and cheap |
Heavy and costly |
| Examples |
Simple voltaic cell, Leclanche cell, Daniel cell, dry cell |
Lead (or acid) accumulator, Ni-Fe (or alkali) accumulator, Li-H battery |
Q5. A torch cell is thrown away once it is finished, while a phone battery is charged and used again for years. What must be different about the chemical change inside the two?
A. The torch cell is a primary cell, in which the chemical reaction is irreversible — once the chemicals are used up, nothing can restore them. A phone battery is a secondary cell, in which the reaction is reversible, so passing current back into it rebuilds the chemicals and stores energy again.
A used cell is not empty — it still holds reactive chemicals inside a thin metal case, which is why cells should never be thrown into a fire or cut open. Heating a sealed cell builds up pressure inside it and can burst the case. Discarded cells also carry metals that should not reach soil or water, so many towns collect them separately rather than with ordinary household waste. The safe habit is simple: take used cells out of a device as soon as it stops working, keep them dry, and hand them in at a collection point instead of binning them.
Collect the cells and batteries lying around your home — torch cells, a remote control, a wall clock, a phone. Copy down the potential difference printed on each and note whether it says ‘rechargeable’. Do not open, heat or connect any of them. You will find the rechargeable ones are all secondary cells.
A shopkeeper offers two cells of the same size for the same appliance. One is marked ‘rechargeable’ and costs far more; the other is marked ‘do not recharge’. State which is the primary cell and which is the secondary cell, and give two properties of each that follow from that answer.
9.8 Symbols Used In Circuit Diagrams
An electric circuit has several electric components connected to a current source. Drawing them as they actually look would be slow and unclear, so physicists agreed long ago on a set of simple symbols. Fig. 9.8-1 shows the real components used in a school laboratory, and the subsections that follow give the symbol and the job of each.
9.8.1 Sources Of Current: Cell, Battery And A.C. Source
The purpose of a source of current is to supply electric current, that is, to maintain the flow of charge in a circuit. There are two types of current source.
The first is a direct current source, such as a cell or a battery. In the laboratory, the Leclanche cell, the Daniel cell and the lead accumulator, or storage cell, are used as direct current sources.
The second is an alternating current source, abbreviated a.c., such as the mains supply in our houses and an a.c. generator. An alternating current is a current in an element, say a bulb, for which both the magnitude and the direction change with time. The current repeats its value after a fixed time, and the number of times the current repeats its value in one second is called the frequency of the alternating current. The frequency of the a.c. obtained from our mains is \(50\\ \\text{Hz}\).
Symbols For The Sources
A d.c. source, that is a cell, is represented by two parallel lines of unequal length, as in Fig. 9.8-2 (a). The longer line is marked ‘+’ and represents the positive terminal, while the shorter line is marked ‘−’ and represents the negative terminal.
It is worth being clear about the path the current takes. When current is drawn from a cell, it flows from the positive terminal to the negative terminal through the external circuit, and from the negative terminal to the positive terminal inside the cell through its electrolyte. Only a closed loop of this kind can maintain a continuous flow.
When a strong current is needed, either we join a number of cells together in series, connecting the negative terminal of one cell to the positive terminal of the next, to form a battery, or we use a storage cell. Fig. 9.8-2 (b) shows the symbol for a battery of three cells.
An alternating current source, that is the mains, is represented by a sine curve drawn inside a circle, as in Fig. 9.8-2 (c).
9.8.2 Keys And Switches
A key is used to put the current on and off in a circuit. It may be a plug key, a switch, or a tapping key. Fig. 9.8-3 gives the symbolic representation of all three, both when they are open and when they are closed. A key is usually represented by the symbol \(K\).
In the laboratory we generally use a plug key. When the key is open, that is when the plug is taken out, the circuit is incomplete and is called an open circuit. When the key is closed, that is when the plug is put in, current flows through the circuit and the circuit is said to be closed. A tapping key is used when current is needed in the circuit only momentarily.
One point of connection matters. The key is always connected in the wire joining the higher potential, that is the positive terminal of the battery.
9.8.3 Resistance Wire, Resistance Box And Rheostat
A resistance wire is generally made from an alloy called manganin. It has a fixed resistance depending upon its length and thickness, and is used as a standard resistance.
Manganin and constantan are chosen for a particular reason. Ordinary metals such as copper gain resistance noticeably as they warm up, which would spoil a standard resistance the moment current passed through it. These alloys are made so that their resistance changes only very slightly with temperature.
The Rheostat
A rheostat is a device by which the resistance in a circuit can be varied continuously. It is used to adjust the magnitude of the current in a circuit by changing the length of the resistance wire included in the circuit.
Its construction is shown in Fig. 9.8-4. It consists of an enamelled constantan wire — constantan is a copper–nickel alloy — wound in the form of a single-layer coil over an asbestos pipe, which is fitted in an iron frame. A sliding contact, called the jockey, moves along a brass rod above the coil. The enamel of the coiled wire is removed at the places where the jockey touches the wire, so that electrical contact is actually made.
A rheostat has three terminals, \(A\), \(B\) and \(C\). Terminals \(A\) and \(B\) are at the two ends of the resistance wire, while terminal \(C\) is at the end of the brass rod that carries the jockey.
The rheostat can be used in two quite different ways, shown in Fig. 9.8-5.
Used as a fixed resistance, connections are made with the terminals \(A\) and \(B\). The wire between these two terminals provides a fixed resistance equal to the resistance of the entire length of wire. The symbol \(R\) is used for a fixed resistance.
Used as a smoothly varying resistance — which is its main use — connections are made between the terminal \(C\) and either of the end terminals \(A\) or \(B\). The current then enters at the end terminal, flows through the resistance wire only as far as the jockey, and leaves at the terminal \(C\). By sliding the jockey and making its contact at different points, a variable resistance is obtained. To attain a current of a desired value in the circuit, the jockey is slid and adjusted until the required resistance is included. The symbol \(Rh\) is used for a variable resistance.
The Resistance Box
A resistance box is provided with several standard resistances — say 1, 2, 5, 10, 20, 20, 50 ohm and so on — connected in series between its two terminals. Each of them is short-circuited by a brass plug.
Pulling out a plug forces the current to go through that particular resistance instead of through the plug. In this way a resistance of any desired value between 1 ohm and its maximum value, which is the sum of all the resistances in the box, can be obtained in steps of one ohm.
Setting A Resistance Box
1. Given: a resistance box containing standard resistances of \(1\\ \\Omega\), \(2\\ \\Omega\), \(2\\ \\Omega\), \(5\\ \\Omega\), \(10\\ \\Omega\) and \(20\\ \\Omega\), all connected in series. Required: a resistance of \(17\\ \\Omega\) in the circuit. To find: which plugs must be taken out.
Rule used: only the resistances whose plugs are removed are included in the circuit, and since they lie in series their values simply add. So we must select a set of the listed values that totals \(17\\ \\Omega\).
Trying the largest value that fits, \(20\\ \\Omega\) is already too big on its own, so it stays plugged. Taking \(10\\ \\Omega\) leaves \(17 - 10 = 7\\ \\Omega\) still needed. Taking \(5\\ \\Omega\) leaves \(7 - 5 = 2\\ \\Omega\) still needed, which one of the \(2\\ \\Omega\) coils supplies exactly.
The plugs of the \(10\\ \\Omega\), \(5\\ \\Omega\) and \(2\\ \\Omega\) resistances must be taken out, and all the others left in. Check: \(10 + 5 + 2 = 17\\ \\Omega\), and \(17\\ \\Omega\) lies between \(1\\ \\Omega\) and the box maximum of \(40\\ \\Omega\), so the setting is possible.
9.8.4 Ammeter And Voltmeter
An ammeter is an instrument used to measure the magnitude of the current flowing in a circuit. It is joined in series in a circuit, so that the entire current of the circuit passes through it. It is represented by the letter \(A\) enclosed in a circle, as in Fig. 9.8-6 (a).
The ‘+’ sign marked at one terminal of the ammeter indicates that current must enter it through that terminal, so that terminal is connected towards the higher potential terminal of the current source. An ammeter must have a very low resistance, so that the resistance of the circuit — and hence the current being measured — is not altered when the ammeter is joined in. It has a calibrated dial on which the deflection of the needle shows the magnitude of the current flowing in that circuit.
A voltmeter is used to measure the potential difference between two points of a circuit. It is connected across the two points between which the potential difference is to be measured, that is, in parallel to the flow of current. It is represented by the letter \(V\) enclosed in a circle, as in Fig. 9.8-6 (b).
Here too the ‘+’ terminal is connected to the point at the higher potential. A voltmeter usually has a very high resistance, so that it does not draw an appreciable current away from the circuit. Its calibrated dial shows the potential difference between the points across which it is connected.
Different kinds of ammeter and voltmeter are required for alternating and for direct quantities. Meters for a.c. work on the heating effect of current, so their graduations are unequally spaced, while meters for d.c. work on the magnetic effect of current, so their graduations are equally spaced.
Table 9.5 — Ammeter Compared With Voltmeter And Galvanometer
| What it does |
Measures the magnitude of current |
Measures the potential difference between two points |
Detects a very weak current and shows its direction |
| Connected |
In series with the component |
In parallel across the component |
In series, like an ammeter |
| Resistance |
Very low |
Very high |
— |
| Terminal marking |
‘+’ terminal towards higher potential |
‘+’ terminal towards higher potential |
No ‘+’ or ‘−’ marked |
| Zero of the scale |
At one end |
At one end |
At the centre |
| Symbol |
\(A\) in a circle |
\(V\) in a circle |
\(G\) in a circle |
9.8.5 Galvanometer
A galvanometer is used when we want to detect the presence of a very weak current in an electric circuit, or to know only the direction of flow of the current. It does not measure the magnitude of the current in a circuit. Like an ammeter, it is joined in a circuit in series, and it is represented by the letter \(G\) enclosed in a circle, as in Fig. 9.8-6 (c).
Current can enter or leave a galvanometer through either of its terminals, so no ‘+’ or ‘−’ signs are marked on them. It has a dial with its zero mark at the centre. The deflection of the needle shows the presence of current, and the side to which the needle deflects indicates the direction of flow of the current.
A galvanometer detects; an ammeter measures. A galvanometer tells you only that a current exists and which way it flows, so its zero sits at the middle of the scale and its terminals carry no signs. An ammeter gives you a value in ampere, so its zero sits at one end.
9.8.6 Load And Connecting Wires
An appliance which is connected in a circuit is called a load. It may be just a resistance, such as a bulb or a heater, or a combination of different electrical components. It is represented by the symbol \(L\), as shown in Fig. 9.8-7.
Connecting wires are the wires used to connect the various electrical components. They are made of a highly conducting metal such as copper, or aluminium because of its low cost, so that they have negligible resistance and do not change the resistance of the circuit.
A connecting wire may be a single thick wire, or several fine wires twisted together. Generally we use thick insulated copper wire as a connecting wire, and in a circuit diagram it is represented simply by a plain line.
The fuel gauge of a car is a rheostat in disguise. A float rides on the surface of the petrol in the tank, and its arm drags a sliding contact along a strip of resistance wire, exactly as a jockey slides along a rheostat coil. A full tank holds the float high and includes only a short length of the wire, so the resistance is small and the current through the gauge is large, swinging the needle towards ‘full’. As the petrol level falls, the float sinks, more of the resistance wire is included, the current drops and the needle falls with it. Nothing in the system measures fuel at all — it measures resistance.
Draw the circuit symbol for each of the following, and state in one line what each is used for: (a) a battery of two cells, (b) a plug key when it is closed, (c) a rheostat used as a variable resistance, (d) a voltmeter.
9.9 Simple Electric Circuit
We now have the source, the symbols and the meters. It is time to put them together into a working circuit, starting with the simplest one there is.
9.9.1 A Cell, A Bulb And A Switch
In our daily life we use a torch, in which a cell — or a combination of two or more cells — is connected to a bulb. This is the simplest electric circuit there is, and it uses only three components: a cell, a bulb and a switch. Fig. 9.9-1 shows the line diagram that represents it.
As the switch is closed, a current flows through the bulb and the bulb glows. The flow of current stops as the switch is opened, and the bulb then ceases to glow.
9.9.2 A Circuit With Ammeter, Voltmeter And Rheostat
Fig. 9.9-2 shows another simple electric circuit, this time carrying the instruments we met in the previous section. Its components are the cell, the key, the rheostat, the bulb, the voltmeter and the ammeter. Here the bulb acts as the load.
Look carefully at how the components are joined. The ammeter, the cell, the key and the rheostat are all in series with the bulb, while the voltmeter is connected in parallel across the bulb.
Two short definitions make those words exact. Electrical components which are joined one after another, and through which the same amount of current flows, are said to be in series. Electrical components which are joined with one terminal forming one end and the second terminal forming the other end are said to be in parallel.
That is why the ammeter goes in series — the whole current of the circuit must pass through it — and why the voltmeter goes in parallel — it must have the two ends of the bulb, and nothing else, across it.
In series, components are joined end to end, so the same current passes through every one of them. In parallel, components are joined side by side across the same two points, so the same potential difference exists across each of them. An ammeter is always in series; a voltmeter is always in parallel.
Demonstrating What Each Component Does
The circuit of Fig. 9.9-2 is worth working through in three stages, because each stage shows one component doing its job. The sequence is summarised in FC 9.4.
(i) First take the plug out of the key. This makes the circuit incomplete, or opens the circuit. The bulb does not glow, and both the ammeter and the voltmeter read zero, since no current flows in the circuit.
(ii) Now insert the plug in the key. The circuit is completed, or closed. The bulb glows, the ammeter reads the current in the circuit, and the voltmeter reads the potential difference, or voltage, across the bulb.
(iii) Then vary the resistance of the circuit by sliding the variable terminal, or jockey, of the rheostat. The glow of the bulb changes, and so do the readings of the ammeter and the voltmeter. On decreasing the resistance by sliding the jockey to the left, the glow of the bulb increases and the readings of the ammeter and voltmeter also increase. On increasing the resistance by sliding the jockey to the right, the glow of the bulb decreases and the readings of the ammeter and voltmeter also decrease.
That last observation is Ohm’s law in front of your eyes. Less resistance in the circuit means more current for the same cell, and a brighter bulb.
Reading A Circuit From Its Meters
1. Given: in a circuit like that of Fig. 9.9-2, the load is a resistance wire kept at a steady temperature. The ammeter reads \(I = 0.4\\ \\text{A}\) and the voltmeter reads \(V = 2.0\\ \\text{V}\). The jockey is then slid until the ammeter reads \(0.2\\ \\text{A}\). To find: (a) the resistance of the wire, and (b) the new voltmeter reading.
Relations used: \(R = \\dfrac{V}{I}\) for part (a), since the ammeter gives the current through the wire and the voltmeter gives the potential difference across that same wire; then \(V = IR\) for part (b), the resistance of the wire itself being unchanged because only the rheostat was moved and the temperature is steady.
- \(R = \\dfrac{2.0\\ \\text{V}}{0.4\\ \\text{A}} = 5\\ \\Omega\). (b) \(V = 0.2\\ \\text{A} \\times 5\\ \\Omega = 1.0\\ \\text{V}\).
The wire has a resistance of \(5\\ \\Omega\), and the voltmeter now reads \(1.0\\ \\text{V}\). This is sensible: halving the current through an unchanged resistance must halve the potential difference across it, and a smaller reading is exactly what sliding the jockey towards more resistance should produce.
Take a working torch and switch it on. Now unscrew the bulb by a quarter turn, just enough to break the contact, and watch it go out even though the switch is still on. Screw it back and it lights again. A single break anywhere in the loop is enough to stop the whole circuit.
A cell, a key, a rheostat and a bulb are joined in series, and a voltmeter is connected across the bulb. State what happens to the reading of the voltmeter, and why, when (a) the key is opened, and (b) the jockey of the rheostat is slid so as to include more of the resistance wire.
9.10 Closed And Open Circuits
Every circuit we have drawn has been a complete loop. That was not a matter of neatness. A loop with a gap in it, however small, is a circuit that does nothing at all.
The path along which current flows is called a circuit. Current flows only if the circuit is complete, or closed. If the circuit is open, or incomplete, current does not flow.
Electric Circuit The closed path along which an electric current flows, made up of a source, connecting wires and one or more components, all of which conduct.
The condition for completeness is worth stating carefully, because it is about the components as much as about the wires. For an electric circuit to be complete, each component of it must pass current through it — that is, every component must be conducting. If there is an insulator anywhere in the path, or if the circuit is broken, the circuit is incomplete, or open, and current will not flow through it.
Three Circuits Compared
Fig. 9.10-1 shows the same dry cell and bulb wired in three different ways, and the difference between them is instructive.
In Fig. 9.10-1 (a), the bulb is connected between the two terminals \(A\) and \(B\) of a dry cell by two metal wires. The circuit is complete, and the bulb glows.
In Fig. 9.10-1 (b), the wire running from terminal \(A\) of the cell to the bulb is broken. The circuit is therefore incomplete, and the bulb does not glow.
In Fig. 9.10-1 (c), terminal \(A\) of the cell is connected to the bulb by a metal wire, but the other terminal \(B\) is connected to the bulb by a thread. A thread is an insulator, so although the loop looks complete to the eye, the circuit is incomplete and the bulb does not glow. Notice that this is the same conclusion as in (b), reached for a different reason — one path has a gap in it, the other has a non-conductor in it.
Q1. The wires of a torch are full of electrons even when the torch is switched off. So why does the bulb light up only at the moment you press the switch?
A. Because a supply of electrons is not enough — they need a complete conducting path and a potential difference to drive them along it. An open switch leaves a gap in the loop, so the circuit is incomplete and no current flows. Closing it completes the path, and the cell’s potential difference at once sets the electrons drifting.
The words sound backwards, so learn them by the gap. An open circuit has an opening in it — a gap or an insulator — so no current flows. A closed circuit is closed up into a complete loop, so current does flow. Open means off; closed means on.
Electricians use a continuity tester, which is nothing more than the circuit of Fig. 9.10-1 with two probe wires left free. Touching the probes to the two ends of a suspect cable completes the loop: if the bulb lights, the cable conducts all the way through, and if it stays dark, there is a break somewhere inside the insulation where no eye could find it. The same trick tests whether a switch really closes, or whether a bulb’s filament has snapped. It is used only on wiring that has first been disconnected from the supply, never on a live circuit, because the tester supplies its own small cell and is meant to be the only source in the loop.
Build the circuit of Fig. 9.10-1 (a) with a torch cell, a torch bulb and two wires. Now break one wire and bridge the gap in turn with a steel spoon, a rubber band, a pencil lead, a dry twig and a coin. Note which of them let the bulb glow. You have sorted the objects into conductors and insulators.
A student joins a cell to a bulb using one copper wire and one length of plastic-coated wire whose plastic coating has not been stripped at either end. State whether the bulb glows, give the reason, and name the one change needed to make the circuit complete.
9.11 Summary
Every substance is made of atoms, which contain electrons, protons and neutrons. Electrons in the inner orbits are held strongly and are called bound electrons; those in the outermost orbit are held weakly, can be detached, and are called free electrons.
Free electrons are the charge carriers in a metal. An atom that loses electrons becomes positively charged, and one that gains electrons becomes negatively charged.
Conductors, such as silver, copper and aluminium, contain a very large number of free electrons, and charge given to a conductor spreads over its entire outer surface. Semiconductors, such as silicon and germanium, contain a moderate number and conduct only to a limited extent, their conductivity rising with temperature or with added impurities. Insulators, such as wood, glass and rubber, contain almost no free electrons, and charge given to them stays where it is placed.
Some materials, cooled below a critical temperature, conduct without any resistance and hence without any loss of energy. This state is superconductivity and such materials are superconductors — mercury, lead, niobium and tin are examples.
Electric charge is denoted by \(q\) or \(Q\), and its SI unit is the coulomb (C). Like charges repel and unlike charges attract. Smaller units are \(1\\ \\text{mC} = 10^{-3}\\ \\text{C}\), \(1\\ \\mu\\text{C} = 10^{-6}\\ \\text{C}\) and \(1\\ \\text{nC} = 10^{-9}\\ \\text{C}\).
By the quantum nature of charge, the charge on a body is always a whole multiple of the electronic charge: \[q = \\pm ne\] where \(q\) is the charge in coulomb (C), \(n\) is a whole number, and \(e = 1.6 \\times 10^{-19}\\ \\text{C}\) is the charge on an electron. A charge such as \(1.5e\) is impossible.
When two conductors are joined by a metal wire, free electrons flow from the conductor of higher electron concentration to the one of lower concentration, and stop when the two concentrations become equal.
A continuous flow requires the excess and the deficit to be maintained. An electric cell does this by a chemical reaction, keeping an excess of electrons on one electrode and a deficit on the other, and so acts as a source of electrons.
Current is the rate of flow of charge across a cross-section normal to the direction of flow. It is a scalar quantity. \[I = \\frac{Q}{t}\] where \(I\) is the current in ampere (A), \(Q\) is the charge in coulomb (C) and \(t\) is the time in second (s).
In metals the current is due to free electrons alone; in electrolytes it is due to both positive ions and negative ions. If \(n\) electrons cross a section in time \(t\), \[Q = n \\times e \\qquad \\text{and} \\qquad I = \\frac{ne}{t}\] with \(n\) a plain count, \(e = 1.6 \\times 10^{-19}\\ \\text{C}\), \(t\) in second (s) and \(I\) in ampere (A).
The SI unit of current is the ampere, where \(1\\ \\text{A} = 1\\ \\text{C s}^{-1}\). A current of \(1\\ \\text{A}\) means \(6.25 \\times 10^{18}\) electrons cross the section each second. Smaller units are \(1\\ \\text{mA} = 10^{-3}\\ \\text{A}\) and \(1\\ \\mu\\text{A} = 10^{-6}\\ \\text{A}\).
A conductor with an excess of electrons is at a negative, or lower, potential; one with a deficit of electrons is at a positive, or higher, potential. Electric potential decides the direction of flow, just as height does for a falling body, level does for water and temperature does for heat.
The rate of flow of electrons in a direction is the electronic current in that direction. The conventional current is taken in the direction of flow of positive charge, and is therefore opposite to the flow of electrons. It flows from higher potential to lower potential, and it is what circuit diagrams mark.
The potential at a point is the work done in bringing a charge from infinity to that point: \[V = \\frac{W'}{q}\] where \(V\) is the potential in volt (V), \(W'\) is the work in joule (J) and \(q\) is the charge in coulomb (C). Potential is a scalar quantity.
The potential difference between two conductors equals the work done in transferring a unit positive charge from one to the other: \[V\_1 - V\_2 = \\frac{W}{q} \\qquad \\text{or} \\qquad W = q \\times V\] with \(W\) in joule (J), \(q\) in coulomb (C) and the potential difference in volt (V). It is a scalar quantity.
The SI unit of potential difference is the volt, where \(1\\ \\text{V} = 1\\ \\text{J C}^{-1}\). The potential difference between two points is 1 volt if 1 joule of work is done in transferring 1 coulomb of charge from one point to the other.
The obstruction offered to the flow of current by a conductor is its electrical resistance. It arises because the drifting electrons repeatedly collide with the fixed positive ions and with other free electrons, losing speed and changing direction at every collision.
Ohm’s law: the current through a conductor is directly proportional to the potential difference across its ends, provided its temperature remains constant. \[R = \\frac{V}{I} \\qquad \\text{or} \\qquad V = IR\] where \(V\) is in volt (V), \(I\) is in ampere (A) and \(R\) is the resistance in ohm (Ω). Resistance is a scalar quantity, and the gradient of a \(V\)–\(I\) graph gives \(R\).
The SI unit of resistance is the ohm, where \(1\\ \\Omega = 1\\ \\text{V A}^{-1}\). A conductor has a resistance of 1 ohm if a current of 1 ampere flows through it when the potential difference across its ends is 1 volt.
The resistance of a wire depends on four things: its material; its length, resistance being proportional to length; its area of cross-section, resistance being proportional to \(1/\\text{area}\); and its temperature, resistance increasing as temperature increases.
Direct current (d.c.) is a current of constant magnitude flowing in one direction, and a cell is its commonest source. A cell has two electrodes in an electrolyte, and converts chemical energy into electrical energy. In an alternating current (a.c.) both the magnitude and the direction change with time; the mains supply has a frequency of \(50\\ \\text{Hz}\).
Primary cells work by an irreversible chemical reaction and cannot be recharged; the simple voltaic cell, Leclanche cell, Daniel cell and dry cell are examples. Secondary cells, or accumulators, work by a reversible reaction and can be recharged; the lead accumulator and the Ni-Fe accumulator are examples.
In a circuit, a key puts the current on and off; a rheostat varies the resistance continuously by changing the length of resistance wire included; a resistance box gives a chosen resistance in steps of one ohm; a load is the appliance connected; and connecting wires of copper have negligible resistance.
An ammeter measures current, is connected in series, and must have a very low resistance. A voltmeter measures potential difference, is connected in parallel across the component, and must have a very high resistance. A galvanometer only detects a weak current and shows its direction, and has its zero at the centre of the scale.
Components joined one after another, carrying the same current, are in series. Components joined across the same two points are in parallel.
Current flows only in a closed, complete circuit, in which every component conducts. A break in the path, or an insulator anywhere in it, leaves the circuit open and no current flows.
9.12 Key Terms
Alternating current (a.c.) — a current whose magnitude and direction both change with time, repeating its value after a fixed time; measured in ampere (A).
Ammeter — an instrument connected in series to measure the magnitude of the current in a circuit; it has a very low resistance.
Ampere (A) — the SI unit of electric current; a current of one ampere flows when one coulomb of charge crosses a section each second.
Battery — two or more cells joined together in series to give a larger potential difference than a single cell.
Bound electrons — the electrons of the inner orbits, held strongly by the nucleus and unable to leave their atom.
Charge carriers — the particles whose movement carries charge through a substance; free electrons in a metal, and ions in an electrolyte.
Conductors — substances containing a very large number of free electrons, through which electric conduction takes place easily.
Connecting wires — wires of a highly conducting metal, usually copper, of negligible resistance, used to join the components of a circuit.
Conventional current — the current taken in the direction of flow of positive charge, and therefore opposite to the flow of electrons; measured in ampere (A).
Coulomb (C) — the SI unit of electric charge.
Direct current (d.c.) — a current of constant magnitude flowing in one direction; measured in ampere (A).
Drift — the slow overall movement of free electrons towards the positive terminal, made up of repeated accelerations broken by collisions.
Electric cell — a source of direct current in which a chemical reaction maintains an excess of electrons on one electrode and a deficit on the other.
Electric charge — the property of a body, gained by losing or gaining electrons, that makes it attract or repel other charged bodies; measured in coulomb (C).
Electric circuit — the closed conducting path along which an electric current flows.
Electric current — the rate of flow of charge across a cross-section normal to the direction of flow; measured in ampere (A).
Electric potential — the quantity that decides the direction of flow of charge between two conductors, measured by the work done in bringing a charge from infinity to a point; measured in volt (V).
Electrical resistance — the obstruction offered to the flow of current by a conductor; measured in ohm (Ω).
Electrodes — the two conducting rods of a cell, held apart in the electrolyte.
Electrolyte — the solution or jelly in a cell in which the electrodes are placed, and with which they react chemically.
Electronic current — the rate of flow of electrons in a given direction; measured in ampere (A).
Elementary charge — the charge on a proton or an electron, the smallest charge found on its own in nature, of magnitude \(1.6 \\times 10^{-19}\\ \\text{C}\).
Free electrons — the loosely held outermost electrons that can be detached from their atoms and move through the substance.
Galvanometer — an instrument connected in series that detects a very weak current and shows its direction; its zero mark lies at the centre of the scale.
Insulators — substances containing almost no free electrons, through which electric conduction does not take place.
Key — a component used to put the current in a circuit on and off; it may be a plug key, a switch or a tapping key.
Load — the appliance connected in a circuit, such as a bulb or a heater.
Ohm (Ω) — the SI unit of resistance; a conductor has a resistance of one ohm if a potential difference of one volt across it drives a current of one ampere.
Ohm’s law — the law that the current through a conductor is directly proportional to the potential difference across its ends, provided its temperature remains constant.
Parallel — an arrangement in which components are joined across the same two points, so that the same potential difference exists across each.
Potential difference — the work done in transferring a unit positive charge from one point to another; measured in volt (V).
Primary cell — a cell that works by an irreversible chemical reaction and therefore cannot be recharged.
Quantum nature of charge — the fact that charge exists only as a whole multiple of the electronic charge, so that \(q = \\pm ne\).
Resistance box — a box of standard resistances joined in series, from which a chosen resistance is obtained in steps of one ohm by removing plugs.
Resistance wire — a wire of an alloy such as manganin, of fixed resistance, used as a standard resistance.
Rheostat — a device whose resistance can be varied continuously, used to adjust the current in a circuit.
Scalar quantity — a quantity having magnitude only; charge, current, potential difference and resistance are all scalars.
Secondary cell — a cell that works by a reversible chemical reaction and can therefore be recharged; also called an accumulator or storage cell.
Semiconductors — substances containing a moderate number of free electrons, which conduct electricity only to a limited extent.
Series — an arrangement in which components are joined one after another, so that the same current passes through each.
Superconductivity — the state in which a material, cooled below its critical temperature, conducts current with no resistance and no loss of energy.
Superconductor — a material that shows superconductivity below its critical temperature; mercury, lead, niobium and tin are examples.
Volt (V) — the SI unit of potential difference; one volt is one joule of work done per coulomb of charge transferred.
Voltmeter — an instrument connected in parallel across two points to measure the potential difference between them; it has a very high resistance.
9.13 Points To Ponder
A copper wire is crowded with free electrons, all of them negatively charged and all of them moving. Yet the wire as a whole is electrically neutral, and a compass or a scrap of paper held near it notices nothing. How can a substance be so full of moving charge and still carry no charge at all?
Electrons drift along a wire remarkably slowly — far slower than you walk. Yet a lamp at the far end of a long wire lights the instant the switch is closed, without any noticeable delay. If it is not the electrons themselves that travel from switch to lamp in that instant, what must be travelling quickly?
Ohm’s law holds only while the temperature of the conductor remains constant, and yet every wire warms a little as soon as current passes through it. In what sense, then, is Ohm’s law ever exactly obeyed, and why is it still one of the most useful relations in physics?
Resistance was explained as the result of electrons colliding with the fixed positive ions of a wire. A superconductor below its critical temperature still contains electrons and still contains ions, and yet offers no resistance whatever. What would have to be true about those collisions for the resistance to disappear completely rather than merely become small?
An ammeter is built to have as little resistance as possible, and a voltmeter to have as much as possible. Suppose the two were accidentally interchanged in a circuit — the ammeter placed across the bulb and the voltmeter in series with it. Reason out what each meter would then read, and what would happen to the bulb.
Charge exists only in whole multiples of \(e = 1.6 \\times 10^{-19}\\ \\text{C}\), so a current is really a stream of separate grains rather than a smooth fluid. Why does no ordinary circuit ever reveal this graininess, and what would have to be true of a current before the individual electrons could be counted one by one?
9.14 Objective Questions
- The charge on a body can never be: (1 mark)
- \(+2e\)
- \(-3e\)
- \(+0.5e\)
- \(-e\)
- In an electrolyte, the current is due to the movement of: (1 mark)
- free electrons only
- positive ions only
- negative ions only
- both positive and negative ions
- A conductor having a deficit of electrons is at a: (1 mark)
- lower, negative potential
- higher, positive potential
- lower, positive potential
- higher, negative potential
- One coulomb of charge is carried by about: (1 mark)
- \(1.6 \\times 10^{-19}\) electrons
- \(6.25 \\times 10^{18}\) electrons
- \(6.25 \\times 10^{-18}\) electrons
- \(1.6 \\times 10^{19}\) electrons
- The gradient of a graph of potential difference against current for a metal wire at constant temperature gives its: (1 mark)
- charge
- power
- resistance
- current
- A voltmeter must have a very high resistance so that it: (1 mark)
- carries the whole current of the circuit
- does not draw an appreciable current from the circuit
- can be connected in series
- reads the current instead of the potential difference
- Which of the following cannot be recharged? (1 mark)
- Lead accumulator
- Ni-Fe accumulator
- Dry cell
- Storage cell
For each of the following, choose from: a. Both A and R are true and R is the correct explanation of A b. Both A and R are true but R is not the correct explanation of A c. A is true but R is false d. A is false but R is true
Assertion (A): A long wire offers more resistance than a short wire of the same material and thickness. Reason (R): The electrons travelling through a longer wire suffer a greater number of collisions. (1 mark)
Assertion (A): An ammeter is always connected in series in a circuit. Reason (R): An ammeter has a very high resistance. (1 mark)
Assertion (A): A galvanometer has its zero mark at the centre of its scale. Reason (R): A galvanometer is used to find the direction of flow of a current as well as to detect it. (1 mark)
Match each quantity in column A with its SI unit in column B. (4 marks)
| a. Electric charge |
i. ohm |
| b. Electric current |
ii. volt |
| c. Potential difference |
iii. coulomb |
| d. Resistance |
iv. ampere |
Fill in the blanks.
- The conventional current in a circuit flows from the ………… potential to the ………… potential. (1 mark)
- Materials that conduct without any resistance below a certain critical temperature are called ………… . (1 mark)
State whether the following statements are true or false.
- The resistance of a metal wire decreases when its temperature rises. (1 mark)
- Current is a scalar quantity. (1 mark)
Name the following: (1 mark each)
- The particles that act as charge carriers in a metal.
- The instrument used to detect a very weak current in a circuit.
- The alloy from which a standard resistance wire is generally made.
Give one word or phrase for each of the following: (1 mark each)
- A current of constant magnitude flowing in one direction.
- The solution or jelly in which the electrodes of a cell are placed.
- A circuit in which there is a break, so that no current flows.
State the SI unit of: (i) electric charge, (ii) potential difference, (iii) resistance. (1 mark each)
Pick the odd one out and give a reason for your choice.
- Pick the odd one out and give a reason: copper, silver, aluminium, rubber. (1 mark)
- Pick the odd one out and give a reason: Leclanche cell, Daniel cell, dry cell, lead accumulator. (1 mark)
9.15 Check Your Concepts
Define electric current, and state its SI unit. (2 marks)
What are free electrons? State why they are called the charge carriers of a metal. (2 marks)
State whether the resistance of the filament of a bulb increases, decreases or stays the same when the bulb begins to glow. Give a reason for your answer. (2 marks)
Give a reason for each of the following: (2 marks each)
- An ammeter is made with a very low resistance.
- Charge given to a conductor spreads over its outer surface, while charge given to an insulator stays where it is placed.
Explain the meaning of the statement, ‘the potential difference between two points is 1 volt’. (2 marks)
Explain the meaning of the statement, ‘the resistance of a wire is 1 ohm’. (2 marks)
Differentiate between a primary cell and a secondary cell, stating the basis of difference in each case. Give one example of each. (3 marks)
Differentiate between conventional current and electronic current, stating the basis of difference. (3 marks)
State Ohm’s law, giving the condition under which it holds. Write the relation between potential difference, current and resistance, naming each symbol and its unit. (3 marks)
Two conductors are joined by a metal wire. One has an excess of electrons and the other has a deficit. Explain which is at the higher potential, and state the direction of flow of electrons and of conventional current. (3 marks)
Explain why a metal wire offers resistance to the flow of current through it. (4 marks)
State the four factors on which the resistance of a wire depends, and explain how the resistance depends on each of them. (4 marks)
Describe how an electric cell is able to maintain a continuous flow of electrons in a circuit, whereas two charged conductors joined by a wire cannot. (4 marks)
What would happen in each of the following cases, and why? (5 marks)
- The plug of the key in a working circuit is taken out.
- One of the two connecting wires between a cell and a bulb is replaced by a cotton thread.
- The jockey of a rheostat in series with a bulb is slid so as to include a longer length of resistance wire.
9.16 Diagrams, Graphs & Constructions
Draw a labelled circuit diagram of a circuit containing a cell, a plug key, a rheostat and a bulb in series, with an ammeter to measure the current in the bulb and a voltmeter to measure the potential difference across it. Mark the direction of the conventional current, and mark the ‘+’ terminal of each meter. (5 marks)
Fig. 9.8-4 shows the construction of a rheostat. Name the parts labelled \(A\), \(B\) and \(C\), and state which pair of terminals is used when the rheostat is required to act as a smoothly varying resistance. (3 marks)
Draw the circuit symbol for each of the following: (i) a battery of three cells, (ii) an a.c. source, (iii) a plug key when open, (iv) a galvanometer, (v) a variable resistance. (5 marks)
Fig. 9.6-2 shows the graph of potential difference against current for a metal wire at constant temperature. State what is plotted on each axis and in what unit, explain what the gradient of the line represents, and state why the line passes through the origin. (4 marks)
Sketch the graph you would expect for the potential difference across a wire of resistance \(10\\ \\Omega\) as the current through it is raised from \(0\) to \(0.5\\ \\text{A}\) at constant temperature. Label both axes with their units, and mark on your sketch the point corresponding to a current of \(0.4\\ \\text{A}\). (4 marks)
Draw a labelled diagram of a simple circuit that could be used to test whether a given material is a conductor or an insulator, using a cell, a bulb and connecting wires. State what you would observe in each case. (4 marks)
9.17 Practice With Numericals
A charge of \(0.6\\ \\text{C}\) passes through a cross-section of a conductor in \(4\\ \\text{s}\). Find the current in the conductor. (2 marks)
A current of \(0.25\\ \\text{A}\) flows through a wire for \(1\\ \\text{minute}\). Find the charge that passes through it. (2 marks)
In transferring a charge of \(3\\ \\text{C}\) through a wire, \(24\\ \\text{J}\) of work is done. Find the potential difference across the ends of the wire. (2 marks)
A potential difference of \(6\\ \\text{V}\) is applied across a resistance of \(12\\ \\Omega\). Find the current that flows through it. (2 marks)
A current of \(0.3\\ \\text{A}\) flows through a wire of resistance \(25\\ \\Omega\). Find the potential difference across the ends of the wire. (2 marks)
A bulb draws a current of \(0.15\\ \\text{A}\) when the potential difference across it is \(4.5\\ \\text{V}\). Find the resistance of its filament while it glows. (2 marks)
A current of \(20\\ \\text{mA}\) flows through a conductor for \(2\\ \\text{minutes}\). Find (i) the charge that passes through it, and (ii) the number of electrons this represents. Take \(e = 1.6 \\times 10^{-19}\\ \\text{C}\). (3 marks)
\(1.5 \\times 10^{19}\) electrons cross a section of a conductor in \(8\\ \\text{s}\). Find (i) the total charge that has passed, and (ii) the current in the conductor. Take \(e = 1.6 \\times 10^{-19}\\ \\text{C}\). (3 marks)
A cell of potential difference \(12\\ \\text{V}\) is connected to a bulb whose filament has a resistance of \(48\\ \\Omega\) while glowing. Find (i) the current drawn from the cell, and (ii) the charge that passes through the filament in \(5\\ \\text{minutes}\). (3 marks)
A cell does \(4.5\\ \\text{J}\) of work in transferring a charge of \(750\\ \\text{mC}\) round a circuit. Find (i) the potential difference across the cell, and (ii) the current that would flow if this cell were connected across a resistance of \(20\\ \\Omega\). (4 marks)