Current-voltage characteristicsAQA A-Level Physics: Revision notes

Section 1

I–V characteristics and Ohm's law

An I–V characteristic is a graph of the current through a component against the pd across it. It shows how the resistance behaves.

Ohm's law states that the current through a conductor is proportional to the pd across it, provided the physical conditions, such as temperature, are constant. It is a special case, not a general law: components that do not obey it can still have a resistance, found at each point from $R = V / I$ .

In these questions the ammeter is ideal (zero resistance) and the voltmeter is ideal (infinite resistance) unless stated otherwise, so they do not change the circuit.

Key termsI–V characteristicOhm's law

Common mistake

Saying that V = I R is Ohm's law. This defines resistance for every component. Ohm's law means R is constant, so I is proportional to V.

Section 2

The ohmic conductor

A metal wire (or fixed resistor) at constant temperature gives a straight line through the origin. The resistance $R = V / I$ is the same at every point and the characteristic is the same in both directions.

With $I$ on the vertical axis, the gradient is $1 / R$ . If $V$ is on the vertical axis instead, the gradient is $R$ . Always check which quantity is on which axis before reading a resistance from a gradient.

Key termsohmic conductor

Exam tip

For a straight line through the origin, the resistance is also V / I at any single point, so you can avoid finding a gradient.

Section 3

The filament lamp

The characteristic of a filament lamp is a curve through the origin that is symmetrical about it. As the pd rises, the current increases less than proportionally, so the resistance increases.

The explanation is the temperature: a larger current heats the filament, so the lattice ions vibrate with larger amplitude, and the conduction electrons collide with them more often. The physical conditions are not constant, so the lamp does not obey Ohm's law.

Key termsfilament

Common mistake

Saying that the resistance of a lamp is the gradient of the I–V curve. The resistance at a point is V / I at that point, not the reciprocal of the gradient of the tangent.

Section 4

The semiconductor diode

A diode allows current in only one direction.

In the forward direction, almost no current flows until the pd reaches a threshold of about 0.6 V. Above this, the current increases rapidly and the resistance falls. In the reverse direction the current is almost zero, so the resistance is very large. The characteristic is not symmetrical and the diode does not obey Ohm's law.

A diode is used to change alternating current into a current in one direction only (rectification).

Key termssemiconductor diodethreshold pd

Section 5

Reading graphs with either axis

Exam questions may put either $I$ or $V$ on the horizontal axis. To avoid errors:

Identify the axes first
For a single point, use $R = V / I$ with values read from the graph
If the line is a straight line through the origin, the resistance is constant
If the curve bends so that V rises faster than I, the resistance is increasing

Worked example: a lamp passes 1.20 A at 4.0 V and 1.80 A at 8.0 V. $R = 4.0 / 1.20 = 3.3$ Ω at 4.0 V and $R = 8.0 / 1.80 = 4.4$ Ω at 8.0 V, so the resistance rises.

Must Know

Ohm's law: I is proportional to V if physical conditions such as temperature are constant
Ohmic conductor: straight line through the origin, constant R
Filament lamp: curve, resistance increases with temperature
Diode: conducts in one direction above about 0.6 V, very high resistance in reverse
R = V / I at any point on any characteristic
Ideal ammeter has zero resistance; ideal voltmeter has infinite resistance

That's the notes covered.

Carry on to the next subtopic.

Exam questions on Current-voltage characteristics

A student investigates a fixed resistor kept at a constant temperature, using an ideal ammeter and an ideal voltmeter. She records a pd of 2.0 V with a current of 4.0 mA, a pd of 4.0 V with a current of 8.0 mA, and a pd of 6.0 V with a current of 12.0 mA. She plots a graph with pd on the vertical axis and current on the horizontal axis.
Calculate the resistance of the resistor at 2.0 V and at 6.0 V, and state what the results show about the resistor.2 marks
Two components, X and Y, are connected in turn to a variable power supply, with an ideal ammeter and an ideal voltmeter. For each component a graph is plotted of pd (vertical axis) against current (horizontal axis). The graph for X is a straight line through the origin with a gradient of 40 Ω. The graph for Y is a curve through the origin whose gradient increases as the current increases.
X is a metal wire. State the condition needed for X to obey Ohm's law, and explain what would happen to the graph for X if the current became large enough to make the wire very hot.2 marks
A technician tests a semiconductor diode with an ideal ammeter and an ideal voltmeter. In the forward direction the current is negligible at 0.50 V, 2.0 mA at 0.70 V and 20 mA at 0.75 V. In the reverse direction, with 5.0 V across the diode, the current is 0.10 μA.
Describe how the current in the diode varies with pd in the forward and reverse directions.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).