Syllabus coverage
- Understand that an electric current is a flow of charge carriers
- Understand that the charge on charge carriers is quantised
- Recall and use Q = It
- Use, for a current-carrying conductor, the expression I = Anvq, where n is the number density of charge carriers
- Define the potential difference across a component as the energy transferred per unit charge, and recall and use V = W / Q
- Recall and use P = VI, P = I^2 R and P = V^2 / R
- Define resistance, and recall and use V = IR
- Sketch the I-V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp, and explain that the resistance of a filament lamp increases as current increases because its temperature increases
- State Ohm's law
- Recall and use R = rho L / A
- Understand that the resistance of a light-dependent resistor decreases as the light intensity increases, and that the resistance of a thermistor decreases as the temperature increases, because thermistors have a negative temperature coefficient
Part of the AS & A Level Physics syllabus 9702.
Charge carriers and the size of a current
An electric current is a flow of charge carriers. In a metal the carriers are the free electrons that are not bound to any particular atom: they wander at random between the fixed positive ions of the lattice, and with no potential difference applied their random motion produces no net transfer of charge in any direction. In an electrolyte the carriers are positive and negative ions, in a semiconductor they are electrons and holes, and in an ionised gas they are electrons and positive ions. Current is measured in amperes (A), and 1 A is a flow of 1 coulomb of charge per second past a point in a circuit.
The size of a current is the rate of flow of charge, so Q = It, where Q is the charge in coulombs, I is the current in amperes and t is the time in seconds. Every carrier is an electron, a proton or an ion, and each of these carries a charge of a fixed size, so charge is quantised: the charge on any body can only be a whole-number multiple of the elementary charge e = 1.60 x 10-19 C. In symbols, Q = Ne, where N is a whole number of carriers. There is no such thing as half an electron's worth of charge on a body, so a measured charge of, say, 3.5 x 10-19 C is impossible.
One coulomb is a large amount of charge in carrier terms. Dividing 1 C by the elementary charge gives 1 / (1.60 x 10-19) = 6.25 x 10^18, so 1 C is the charge carried by 6.25 x 10^18 electrons. A steady current of 0.20 A flowing for 30 s transfers Q = It = 0.20 x 30 = 6.0 C, which is 6.0 / (1.60 x 10-19) = 3.8 x 10^19 electrons. Notice that you always divide the total charge by the charge on one carrier to find how many carriers passed.
Conventional current is the direction in which positive charge would flow: round the circuit from the positive terminal of the source to the negative terminal. In a metal the electrons are negative, so they drift the opposite way, from the negative terminal round to the positive terminal. Both descriptions describe the same circuit, and either may be used in a calculation, but if a question asks about the direction of the electron flow, the answer is always opposite to the conventional current.
- In a metal the charge carriers are free electrons; in a solution they are ions; in a semiconductor they are electrons and holes.
- Q = It: charge in coulombs = current in amperes x time in seconds.
- Charge is quantised, Q = Ne, with e = 1.60 x 10-19 C and N a whole number.
- 1 C is the charge on 6.25 x 10^18 electrons.
- Electrons drift from the negative terminal to the positive terminal, opposite to the conventional current.
Drift velocity and the equation I = Anvq
With no potential difference across a metal, the free electrons move randomly at high speed, of the order of 10^5 m s-1, but they make no progress along the wire. When a p.d. is applied, an electric field is set up inside the conductor and each electron feels a force, so it accelerates briefly along the wire until it collides with a lattice ion and loses most of its speed. The average velocity along the wire, superimposed on the random motion, is the mean drift velocity, typically only of the order of 10-4 m s-1.
The link between the current and the carriers can be derived by counting the charge that passes a cross-section. Take a conductor of cross-sectional area A containing n charge carriers per cubic metre, each carrying charge q, all drifting at speed v. In a time t the carriers inside a cylinder of length v t pass the cross-section: its volume is A v t, so it contains n A v t carriers, carrying a total charge of n A v t q. The current is the rate of flow of charge, so I = Q / t = n A v t q / t, which gives I = Anvq.
Each symbol carries a physical meaning you will be asked to name. A is the cross-sectional area in m2, n is the number density of charge carriers in m-3, v is the mean drift velocity in m s-1 and q is the charge on one carrier in coulombs (1.60 x 10-19 C for an electron). For copper the number density is about 8.5 x 10^28 m-3, which is roughly one free electron per atom. A copper wire of cross-sectional area 2.0 x 10-6 m2 carrying 2.72 A therefore has v = I / (Anq) = 2.72 / (2.0 x 10-6 x 8.5 x 10^28 x 1.60 x 10-19) = 2.72 / (2.72 x 10^4) = 1.0 x 10-4 m s-1.
Two consequences follow from I = Anvq. If a wire narrows and the current stays the same, A falls so v must rise: the carriers have to move faster through the narrower part. And although the electrons themselves creep along, every free electron in the circuit, including those already sitting in a lamp filament, starts to drift almost at once when the switch is closed. That is because the electric field is established throughout the circuit at close to the speed of light, 3.00 x 10^8 m s-1, so the lamp lights immediately even though no electron has travelled from the battery to the lamp.
- In time t the carriers in a length v t pass a cross-section: number = nAvt, charge = nAvtq, so I = Anvq.
- n is the number density of carriers in m-3; A must be in m2 and q is the charge on one carrier.
- The mean drift velocity of electrons in a metal is of the order of 10-4 m s-1, far smaller than their random speed of about 10^5 m s-1.
- A circuit switches on almost instantly because the electric field is set up at close to the speed of light, not because the electrons are fast.
| Symbol | Quantity | Unit | Typical value for a copper wire |
|---|---|---|---|
| A | Cross-sectional area of the conductor | m2 | 2.0 x 10-6 m2 |
| n | Number density of charge carriers | m-3 | 8.5 x 10^28 m-3 |
| v | Mean drift velocity of the carriers | m s-1 | 1.0 x 10-4 m s-1 |
| q | Charge on one charge carrier | C | 1.60 x 10-19 C |
Potential difference: energy transferred per unit charge
The potential difference across a component is defined as the energy transferred per unit charge passing through it. If 1 coulomb of charge passes through a component and 1 joule of energy is transferred, the p.d. across the component is 1 volt, so V = W / Q, where W is the energy transferred in joules and Q is the charge in coulombs. The unit follows directly from the definition: 1 V = 1 J C-1.
The energy is transferred from electrical form to other forms inside the component: in a resistor it becomes thermal energy, in a lamp it becomes light and thermal energy, in a motor it becomes kinetic energy of the moving parts plus some thermal energy. The p.d. is a property of the component and is measured across it with a voltmeter in parallel, whereas the current is the rate of flow of charge through it and is measured with an ammeter in series. Keeping those two words right is part of the physics, not just the grammar.
Multiplying V = W / Q by Q = It gives the energy transferred in a given time: W = VIt. In a simple circuit the source, whether a cell, a battery or a generator, transfers energy to the charge carriers, so they leave it carrying energy which they then deliver to the components round the rest of the circuit. The energy transferred per unit charge by the source is its electromotive force, and it is the p.d. of the source that drives the current round the circuit.
A worked example pins the definition down. A component with a p.d. of 6.0 V across it carries a current of 2.0 A for 30 s. The charge that passes is Q = It = 2.0 x 30 = 60 C, and the energy transferred is W = QV = 60 x 6.0 = 360 J. The same answer comes from W = VIt = 6.0 x 2.0 x 30 = 360 J, which is exactly what you should expect, because both expressions come from the same definition.
- Potential difference across a component = energy transferred per unit charge, V = W / Q; 1 V = 1 J C-1.
- W = QV, and because Q = It, the energy transferred is also W = VIt.
- The p.d. is measured across a component with a voltmeter in parallel; the current is measured through it with an ammeter in series.
- Example: at 6.0 V, 60 C of charge transfers W = QV = 60 x 6.0 = 360 J to the component.
Electrical power: P = VI, P = I^2 R and P = V^2 / R
Power is the rate of energy transfer, P = W / t. Substituting W = QV and Q = It into that gives P = QV / t = (It)V / t, so P = VI: the power transferred by a component is the product of the potential difference across it and the current through it. For a lamp marked 12 V, 36 W, the working current is I = P / V = 36 / 12 = 3.0 A.
The other two forms come from substituting V = IR into P = VI. Replacing V gives P = (IR)I, so P = I^2 R; replacing I instead gives P = V(V / R), so P = V^2 / R. All three equations describe the same power, and for an ohmic component at constant temperature they give identical answers - the choice is simply a matter of which two quantities you know.
The form you choose matters in practice. Use P = VI when you know the p.d. and the current, P = I^2 R when you know the current and the resistance (this is the form for the power wasted as heat in a cable, or for the output of a heating element of known resistance), and P = V^2 / R when you know the p.d. across a component and its resistance. Continuing the lamp example: its resistance is R = V / I = 12 / 3.0 = 4.0 ohm, and R = V^2 / P = (12 x 12) / 36 = 4.0 ohm confirms it.
Energy is power multiplied by time, W = Pt, so the 36 W lamp left on for 5.0 minutes transfers W = 36 x (5.0 x 60) = 36 x 300 = 1.08 x 10^4 J. Because the wasted power in a cable is I^2 R, the loss rises with the square of the current: doubling the current quadruples the energy wasted as heat. That is why electrical energy is transmitted through the grid at a high p.d. and a small current, using transformers to raise and lower the p.d.
- P = W / t and W = QV, so P = VI.
- Substituting V = IR into P = VI gives P = I^2 R; substituting I = V / R gives P = V^2 / R.
- Energy transferred W = Pt, so a 36 W lamp running for 300 s transfers 1.08 x 10^4 J.
- Wasted power in a cable is I^2 R, so doubling the current quadruples the loss.
| Equation | Use it when you know | Typical use |
|---|---|---|
| P = VI | The p.d. across the component and the current through it | The power drawn by a lamp or an appliance from a supply of known p.d. |
| P = I^2 R | The current and the resistance | The power wasted as heat in a cable, where the current is fixed by the load |
| P = V^2 / R | The p.d. across the component and its resistance | The power of a heater element connected to a supply of known p.d. |
Resistance and Ohm's law
The resistance of a component is the potential difference across it divided by the current through it: R = V / I. It tells you how much p.d. is needed for each ampere, so for a fixed p.d. a large resistance means a small current. The unit is the ohm, and 1 ohm = 1 V A-1. Resistance is not the same as the energy transferred: a component of low resistance can transfer a great deal of energy if a large current flows through it.
Ohm's law is a separate statement: the current through a conductor is proportional to the potential difference across it, provided physical conditions, in particular the temperature, remain constant. When I is proportional to V the ratio V / I is a constant, so the resistance is constant, and a graph of current against p.d. is a straight line through the origin. Any conductor that behaves this way is described as ohmic.
This is where the marks are lost: R = V / I is a definition, not Ohm's law. You can calculate V / I for anything, including a lamp or a diode, and get a number. Ohm's law is the extra information that the number stays the same as the p.d. is changed, and that is true only when the temperature does not change.
Temperature matters because it is the collisions between the drifting electrons and the vibrating lattice ions that limit the current. Raise the temperature and the ions vibrate with larger amplitude, so collisions are more frequent and a larger p.d. is needed for the same current: the resistance rises. That is why a metallic conductor obeys Ohm's law only while the current is small enough to leave the temperature unchanged, and why resistors made from constantan or nichrome are used in the laboratory - their resistance changes very little over the range of temperatures a student's circuit produces.
- Resistance = p.d. across the component / current through it, R = V / I, measured in ohms (1 ohm = 1 V A-1).
- Ohm's law: the current through a conductor is proportional to the p.d. across it, provided the temperature is constant.
- I is proportional to V exactly when R is constant, so an ohmic component has a straight-line I-V graph through the origin.
- R = V / I applies to every component; it is not a statement of Ohm's law.
I-V characteristics of a metal, a filament lamp and a diode
To obtain an I-V characteristic, the component is connected in series with a cell (or low-voltage supply), a variable resistor and an ammeter, with a voltmeter connected in parallel across the component. Adjusting the variable resistor changes the p.d. across the component, and each pair of readings is recorded. Reversing the connections to the component, or reversing the supply, gives the negative values, and the readings are plotted with current on the y-axis and p.d. on the x-axis.
A metallic conductor at constant temperature gives a straight line through the origin: doubling the p.d. doubles the current. Its gradient is I / V, so 1 / gradient is the resistance, and because the line is straight the resistance is the same at every point. This is the shape required by Ohm's law, and it is what a constantan or nichrome resistor produces as long as the current is kept small enough not to heat it.
A filament lamp gives a curve through the origin whose gradient decreases as the p.d. rises. At each point the resistance is R = V / I, and working through the readings shows R increasing - it is much larger at full brightness than when the filament is cold. The reason is temperature: a larger current transfers more energy to the tungsten filament, so it becomes white hot; the vibrating metal ions collide with the drifting electrons more often, so the current increases less and less for equal increases in p.d. A lamp is therefore deliberately non-ohmic.
A semiconductor diode behaves quite differently. In the forward direction the current is almost zero until the p.d. reaches about 0.6 V for a silicon diode; beyond that threshold the current rises extremely steeply, so the resistance falls to a small value. In the reverse direction there is only a tiny leakage current, so the resistance is very large indeed, until at a large enough reverse p.d. the diode breaks down. Because the ratio V / I is different for every pair of readings, a diode does not obey Ohm's law, and its characteristic is not symmetrical about the origin.
- Plot current on the y-axis against p.d. on the x-axis, and take readings in both directions by reversing the connections.
- Metal at constant temperature: straight line through the origin, constant resistance.
- Filament lamp: curve with a falling gradient, because the hotter filament has a higher resistance.
- Diode: negligible current below about 0.6 V forward, then a very steep rise; only a leakage current in reverse.
| Component | Shape of the I-V graph | Resistance | Ohmic? |
|---|---|---|---|
| Metal conductor at constant temperature | Straight line through the origin | Constant | Yes, provided the temperature does not change |
| Filament lamp | Curve through the origin with the gradient falling as the p.d. rises | Increases as the current and the temperature rise | No |
| Semiconductor diode | Almost no current in reverse; no current until about 0.6 V forward, then a very steep rise | Very large in reverse, very small once forward conducting | No |
Resistivity and the equation R = rho L / A
The resistance of a wire depends on its dimensions and on its material. Experiments with wires of the same material show that R is proportional to the length L and inversely proportional to the cross-sectional area A, so R is proportional to L / A. Writing the constant of proportionality as the material's resistivity rho gives R = rho L / A, and rearranging shows that rho = RA / L. The unit of resistivity follows from that rearrangement: ohm x m2 / m = ohm m.
The two proportionalities have a clear physical reason. Doubling the length doubles the number of collisions a carrier suffers as it travels the length of the wire, so twice the p.d. is needed for the same current. Doubling the cross-sectional area gives twice as many paths for the carriers, so half the p.d. produces the same current. Resistivity is a property of the material alone: a short thick copper wire and a long thin copper wire have very different resistances but exactly the same resistivity, because rho is fixed by the material and its temperature, not by its shape.
The values in the table show how large the differences between materials can be. Copper is used for connecting wires and for the cables of the grid because its resistivity is low, while nichrome, with a resistivity about sixty times larger, is used for heating elements because it dissipates energy readily and resists oxidation at high temperature. A superconductor has zero resistivity below its critical temperature; a semiconductor such as germanium or silicon has a resistivity that falls as the temperature rises, and a thermistor or an LDR exploits exactly that behaviour.
A worked example, and the unit conversion that goes with it. A uniform constantan wire 2.00 m long has a cross-sectional area of 5.00 x 10-7 m2 and a measured resistance of 1.96 ohm, so rho = RA / L = (1.96 x 5.00 x 10-7) / 2.00 = 4.9 x 10-7 ohm m, which is the accepted value for constantan. If the area had been quoted as 0.50 mm2 you would first convert the length unit and then square it: 1 mm2 = (1 x 10-3 m)2 = 1.0 x 10-6 m2, so 0.50 mm2 = 0.50 x 1.0 x 10-6 = 5.0 x 10-7 m2.
- R = rho L / A, so rho = RA / L, measured in ohm m.
- R is proportional to the length and inversely proportional to the cross-sectional area, but rho is a property of the material alone.
- Convert an area from mm2 to m2 by squaring the length conversion: 1 mm2 = 1 x 10-6 m2.
- Example: a 2.00 m length of constantan of area 5.00 x 10-7 m2 with resistance 1.96 ohm has rho = 4.9 x 10-7 ohm m.
| Material | Resistivity / ohm m | Where it is used |
|---|---|---|
| Copper | 1.7 x 10-8 | Connecting wires, motor windings and power cables, because the resistance and the wasted power are low |
| Aluminium | 2.6 x 10-8 | Overhead power lines, because it is much less dense than copper so a thicker conductor can be supported |
| Tungsten | 5.6 x 10-8 | Lamp filaments, because it has a very high melting point and will glow white hot |
| Constantan | 4.9 x 10-7 | Standard laboratory resistors, because its resistance hardly changes with temperature |
| Nichrome | 1.1 x 10-6 | Heating elements in kettles, toasters and heaters, because it has a high resistivity and does not oxidise |
Thermistors and light-dependent resistors: materials that change their resistance
A thermistor is made from a semiconductor. Electrons in a semiconductor are not all free to move, and raising the temperature gives more of them enough thermal energy to break free from their atoms. The number density n of charge carriers therefore increases as the temperature rises, and from I = Anvq a larger n means a larger current for the same p.d., so the resistance falls. Because its resistance falls as the temperature rises, the thermistor is described as having a negative temperature coefficient (NTC).
This is the opposite of what happens in a metal. In a metal the number of free electrons is essentially fixed at about one per atom, so heating cannot increase n much; instead it makes the lattice ions vibrate with larger amplitude, so the electrons collide with them more often and the resistance rises. The same rise in temperature therefore pushes the resistance of a metal up and the resistance of a semiconductor down, and the different reason in each case is what an explanation question is looking for.
A light-dependent resistor (LDR) is also a semiconductor, usually made from cadmium sulphide. In the dark its resistance is very high, often millions of ohms. When light falls on it, the photons transfer energy to electrons in the material and free them, so again n increases, the current for a given p.d. increases, and the resistance falls. The greater the light intensity, the more carriers are released and the lower the resistance.
Both sensors are used because their resistance can be turned into a change in p.d. and then into a switching or measuring action. A thermistor in a thermostat keeps an oven, a fridge or an incubator at a steady temperature by switching the heating or cooling on and off, and thermistors are also used as the sensing element of electronic thermometers. An LDR switches street lamps on at dusk, forms the light meter of a camera and sounds an alarm when a light beam is broken, because in each case a change in light intensity produces a predictable change in resistance.
- NTC thermistor: resistance falls as temperature rises, because the number density of charge carriers increases.
- LDR: resistance falls as light intensity increases, again because more charge carriers are released.
- Metal: resistance rises with temperature, because the ions vibrate more and collisions are more frequent.
- The crucial test in an answer is why the resistance changes: I = Anvq is used for the thermistor and the LDR, and the collision rate is the reason in a metal.
| Sensor | What is changed | Effect on the resistance | Reason |
|---|---|---|---|
| NTC thermistor | A rise in temperature | Resistance falls | More electrons break free from their atoms, so the number density n of charge carriers increases |
| LDR | A rise in light intensity | Resistance falls | Photons release more electrons, so the number density n of charge carriers increases |
| Metallic resistor | A rise in temperature | Resistance rises | The lattice ions vibrate with larger amplitude, so the carriers collide with them more often |
Key terms you must be able to define
- Electric current
- A flow of charge carriers; its size is the rate of flow of charge, I = Q / t, measured in amperes, where 1 A is a flow of 1 C per second past a point in the circuit.
- Charge carrier
- A charged particle whose movement constitutes an electric current: free electrons in a metal, positive and negative ions in an electrolyte, and electrons and holes in a semiconductor.
- Quantisation of charge
- The charge on any body can only be a whole-number multiple of the elementary charge e = 1.60 x 10-19 C, so Q = Ne with N a whole number.
- Mean drift velocity
- The average velocity of the charge carriers along the conductor caused by the applied electric field; in a metal it is of the order of 10-4 m s-1, far smaller than the random speed of the electrons.
- Number density
- The number of charge carriers per unit volume of a material, symbol n, measured in m-3; for copper it is about 8.5 x 10^28 m-3.
- Potential difference
- The energy transferred per unit charge passing through a component, V = W / Q; measured in volts, where 1 V = 1 J C-1.
- Resistance
- The potential difference across a component divided by the current through it, R = V / I; measured in ohms, where 1 ohm = 1 V A-1.
- Ohm's law
- The current through a conductor is proportional to the potential difference across it, provided physical conditions such as temperature remain constant; a conductor that behaves in this way has a constant resistance and a straight-line I-V graph through the origin.
- Resistivity
- The resistance of a sample of a material of unit length and unit cross-sectional area, rho = RA / L, measured in ohm m; it is a property of the material and its temperature alone, not of the shape of the sample.
- Negative temperature coefficient (NTC) thermistor
- A semiconductor component whose resistance decreases as its temperature increases, because the number density of charge carriers rises as more electrons are freed by the greater thermal energy.
- Light-dependent resistor (LDR)
- A semiconductor component whose resistance decreases as the light intensity falling on it increases, because photons release more charge carriers, increasing the number density n.
Applied to the real world
Cambridge sets 9702 in unfamiliar contexts - a fairground ride, a power station, a hospital scanner, a satellite, an astronomical observatory. Use these as models for how to apply the physics, then write your own.
You obtain the I-V characteristic of a filament lamp by connecting the lamp in series with a cell, a variable resistor and an ammeter, and putting a voltmeter in parallel across the lamp. As you wind the variable resistor to raise the p.d., the current readings become more widely spaced instead of equally spaced, and the graph curves over instead of staying straight. Reversing the lamp gives the same curve on the other side of the origin, which shows the lamp is non-ohmic. The gradient falls because the filament gets hotter: a typical tungsten filament has a resistance about ten times greater when it is lit than when it is cold, which is also why the surge of current at switch-on can blow the filament.
Overhead power lines use aluminium conductors around a steel core. Aluminium has a resistivity of about 2.6 x 10-8 ohm m, a little higher than the 1.7 x 10-8 ohm m of copper, but it is far less dense, so a thicker, lower-resistance cable can be strung between pylons without the towers having to carry too much weight. The power wasted as heat in the cable is I^2 R, so the loss rises with the square of the current: doubling the current quadruples the wasted power for the same cable, which is why the grid is designed to carry a high p.d. and a small current.
A car headlamp bulb is a filament lamp whose cold resistance is far lower than its resistance when it is lit. With a 12 V supply and a bulb rated at 60 W, the current when working is I = P / V = 60 / 12 = 5.0 A and the resistance is R = V / I = 12 / 5.0 = 2.4 ohm. When the bulb is cold its resistance may be only about a tenth of that, so the very first instant after the switch is closed sends a current several times larger than 5.0 A through the filament.
NTC thermistors are the sensing element in electronic clinical thermometers and in the temperature-control circuits of incubators and ventilators. The thermistor is placed in a circuit whose output p.d. depends on the resistance, so a small change in the patient's temperature produces a measurable change in p.d. that can be read from a display or used to switch a heater on and off. A thermistor is chosen rather than a metal resistor because the fractional change in resistance with temperature is much larger, so the instrument is more sensitive.
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Exam technique for this topic
- Learn the two definitions exactly. Resistance is the potential difference across the component divided by the current through it, and the potential difference across a component is the energy transferred per unit charge. 'A measure of how hard it is for current to flow' scores nothing.
- Never confuse the definition R = V / I with Ohm's law. R = V / I works for every component, ohmic or not; Ohm's law is the extra statement that the current is proportional to the p.d. at constant temperature. If a question asks whether a component obeys Ohm's law, the answer must mention the shape of the graph and constant temperature.
- Convert units before you substitute. An area in mm2 must be converted by squaring the length conversion, so 1 mm2 = (1 x 10-3 m)2 = 1 x 10-6 m2, and 0.50 mm2 = 5.0 x 10-7 m2. Writing 0.50 mm2 as 0.50 x 10-3 m2 makes the resistance a thousand times too small and costs the whole calculation.
- Choose the power equation that matches the data you are given: P = VI when you know the p.d. and the current, P = I^2 R when you know the current and the resistance (the form to use for the power wasted in cables), and P = V^2 / R when you know the p.d. and the resistance. Quote the equation, substitute, then give the answer with its unit.
- In an I-V question, state the axes (current on the y-axis, p.d. on the x-axis) and describe the shape precisely: a straight line through the origin for a metal at constant temperature, a curve with a falling gradient for a filament lamp, and for a silicon diode only a leakage current in reverse and a very steep rise after about 0.6 V in the forward direction. For a curved graph, work out the resistance from the coordinates of a point using R = V / I, never from the gradient.
- When you use I = Anvq, check every symbol: n is a number density in m-3, A is in m2, q is the charge on one carrier, 1.60 x 10-19 C, and v comes out in m s-1. A metal gives a drift velocity of the order of 10-4 m s-1; an answer close to the speed of light means a wrong n or a wrong q has been used.
Why students lose marks here
Where this fits in AS & A Level Physics
This page is one topic of Cambridge AS & A Level Physics 9702. AS & A Level Physics is the course home: every area and every topic in Cambridge's own order, the papers you sit and what each one tests, and the exam-practice tools. The full topic list, with each topic linked to its revision page, is on the AS & A Level Physics syllabus page.