OCR GCSE Physics A: Resistance, Ohm's law and I-V characteristics (J249)

This guide is written for OCR GCSE (9-1) Gateway Science Physics A (J249), Version 5.0 (July 2026), and covers statements P3.2c to P3.2h in topic P3, Electricity (the simple circuits section). None of these statements is marked as Higher Tier only, so everything here is for Foundation and Higher candidates. Series and parallel calculations, power and charge flow are taught elsewhere, so they are left out. Pair this page with the revision notes and the practice questions. See also the OCR GCSE Physics hub and the printable checklist. Start with the free 10-minute diagnostics. For paper technique, see OCR GCSE Physics exam preparation.

What this unit covers

Statement	What you must be able to do
P3.2c	Recall that current depends on resistance and p.d., and the units used, including the definition of potential difference
P3.2d	Recall and apply V = IR
P3.2e	Explain that some resistors keep a constant R while others change as the current changes
P3.2f	Describe and justify how circuits are built and used to investigate these effects, with wires of different lengths, filament lamps, diodes, NTC thermistors and LDRs
P3.2g	Use graphs to decide whether a circuit element is linear or non-linear
P3.2h	Use graphs and relate the curves to the function and properties of those elements

Current, p.d. and resistance (P3.2c)

Three quantities describe what a component does in a circuit.

Quantity	Symbol	Unit	Unit symbol
Current	I	ampere	A
Potential difference (p.d.)	V	volt	V
Resistance	R	ohm	Ω

Potential difference is the energy transferred per unit charge as charge moves between two points in a circuit. A p.d. of 1 volt means 1 joule of energy is transferred for each coulomb of charge that passes. A cell or power supply provides the p.d. that pushes charge round the circuit. Resistance measures how hard it is for charge to flow through a component.

The link between them is simple. For a given component, a larger p.d. gives a larger current. For a given p.d., a larger resistance gives a smaller current. Current is measured with an ammeter connected in series. P.d. is measured with a voltmeter connected in parallel across the component.

A common misconception is to think current gets “used up” or that p.d. is something that flows. Current is the flow of charge. P.d. is the energy transfer per unit charge between two points, so it is always measured across something.

V = IR (P3.2d)

potential difference (V) = current (A) × resistance (Ω)

The three versions are:

• V = I × R, to find the p.d.
• I = V ÷ R, to find the current.
• R = V ÷ I, to find the resistance.

Use a triangle with V on top and I and R below if that helps, but always write the equation you are using and then substitute.

Worked example 1. A resistor has 0.045 A flowing through it when the p.d. across it is 9.0 V. Find its resistance.

R = V ÷ I = 9.0 ÷ 0.045 = 200 Ω

Worked example 2. A 470 Ω resistor is connected across a 12 V supply. Find the current in mA.

I = V ÷ R = 12 ÷ 470 = 0.0255 A (3 significant figures) = 25.5 mA

Worked example 3. A current of 0.35 A flows through a component of resistance 18 Ω. Find the p.d. across it.

V = I × R = 0.35 × 18 = 6.3 V

Watch the units. Convert milliamperes to amperes (divide by 1000) and kilohms to ohms (multiply by 1000) before you substitute, or keep consistent units such as kΩ with mA, which give volts.

Constant and changing resistance (P3.2e)

V = IR is true for every component at every moment, because it defines the resistance at that moment. What differs between components is whether R stays the same as the current changes.

• Constant resistance. A fixed resistor, or a metal wire at constant temperature, has the same R whatever the p.d. When p.d. doubles, current doubles. These are called ohmic conductors.
• Changing resistance. A filament lamp, a diode, a thermistor and an LDR all have a resistance that depends on conditions, so the ratio V ÷ I is not the same at every point.

Resistance of a metal wire also depends on its dimensions. A longer wire has a larger resistance, because charge meets more of the wire’s atoms on its way through. For a wire of the same material and thickness at constant temperature, resistance is directly proportional to length. A thicker wire has a smaller resistance, because there is more room for charge to flow.

Worked example 4: wire length. A student keeps the current at 0.50 A through different lengths of one wire and measures the p.d. across each.

Length (m)	P.d. (V)	R = V ÷ I (Ω)
0.20	0.60	1.2
0.40	1.20	2.4
0.60	1.80	3.6
0.80	2.40	4.8

Each time the length doubles or triples, R does too, so R is proportional to length. For 1.00 m, R = 6.0 Ω.

Designing circuits to explore these effects (P3.2f)

The specification suggests building circuits and measuring current and p.d., recording the p.d. across and current through different components to calculate resistances, and investigating how the length of a wire affects its resistance.

Basic test circuit.

1. Connect the component in series with a cell or power supply, an ammeter and a variable resistor.
2. Connect the voltmeter in parallel across the component only, not across the ammeter or the supply.
3. Change the variable resistor to alter the current. Record several pairs of V and I.
4. Calculate R = V ÷ I for each pair.

Using more or fewer cells in the supply also changes the p.d. For a full I-V graph that includes negative values, swap the connections to the supply (or reverse the cell) so that the current and p.d. are reversed, then take more readings.

Control and accuracy.

• Wires and resistors heat up when current flows. Use small currents, and switch off between readings, so a wire stays at constant temperature.
• Repeat readings and take a mean, and check meters for a zero error before you start.
• For a diode, include a fixed resistor in series so the current cannot become large enough to damage it.
• For a thermistor, place it in a water bath and read the temperature with a thermometer as you heat or cool it. For an LDR, change the light intensity falling on it, for example by moving a lamp towards or away from it, and keep other light constant.

I-V graphs: linear or non-linear (P3.2g)

An I-V graph plots current on the vertical axis against p.d. on the horizontal axis. Plot the points, then draw a smooth line or curve of best fit, not dot-to-dot.

• A linear element gives a straight line through the origin. Its resistance is constant.
• A non-linear element gives a curve, or a line that is not straight through the origin. Its resistance changes.

Resistance at any point is R = V ÷ I for that point. With current on the vertical axis, the gradient of a straight line equals 1 ÷ R, so a steeper line means a smaller resistance. Do not use the gradient of a curve as the resistance. Read V and I at the point you want and divide.

Worked example 5: a lamp’s readings.

P.d. (V)	Current (A)	R = V ÷ I (Ω)
1.0	0.20	5.0
2.0	0.34	5.9
3.0	0.45	6.7
4.0	0.54	7.4
5.0	0.62	8.1
6.0	0.68	8.8

Resistance is not constant, so the lamp is non-linear. The line of best fit bends towards the p.d. axis because each extra volt produces a smaller extra current.

Linking the curves to the component (P3.2h)

Element	Shape of I-V graph	What happens to R	Why / use
Fixed resistor, wire at constant temperature	Straight line through origin, same in both directions	Constant	Ohmic conductor
Filament lamp	Curve, flattening as p.d. rises, rotationally symmetrical through the origin	Increases as current rises	The filament gets hotter
Diode	Almost no current in the reverse direction. In the forward direction, almost none until a small p.d. is reached, then a steep rise	Very large in reverse, small once conducting	Allows current in one direction only
NTC thermistor	Curve that steepens if the current heats it	Decreases as temperature rises	Temperature sensing, such as a fire alarm or thermostat
LDR	Steeper line at higher light intensity	Decreases as light intensity rises	Light sensing, such as automatic lights

Why a lamp’s resistance rises. Charge carriers in a metal are free electrons. A larger current heats the filament, so the metal’s ions vibrate more. Electrons collide with them more often, which makes it harder for charge to flow, and resistance increases.

Diodes. A diode is used where current should only flow one way, for example to protect a circuit if a battery is connected the wrong way round. Its graph is not symmetrical, because the two directions behave differently.

Worked example 6: a diode. Suppose a diode carries 20 mA at 0.70 V forward and 2 mA at 0.60 V forward (data supplied in a question).

At 0.70 V: R = 0.70 ÷ 0.020 = 35 Ω. At 0.60 V: R = 0.60 ÷ 0.002 = 300 Ω. The resistance has fallen sharply as the p.d. rose, so the diode is non-linear.

Worked example 7: a thermistor. An NTC thermistor is connected across 6.0 V. Its resistance is 2000 Ω at 20 °C and 400 Ω at 60 °C.

At 20 °C: I = 6.0 ÷ 2000 = 0.0030 A = 3.0 mA. At 60 °C: I = 6.0 ÷ 400 = 0.015 A = 15 mA. Resistance falls as temperature rises, so the current is five times larger. That is why a thermistor can drive a temperature-controlled circuit.

Worked example 8: an LDR. An LDR is connected across 5.0 V. In the dark its resistance is 500 kΩ. In bright light it is 2 kΩ.

Dark: I = 5.0 ÷ 500 000 = 0.000 010 A = 10 µA. Bright: I = 5.0 ÷ 2000 = 0.0025 A = 2.5 mA. Resistance falls as light intensity rises.

Common errors

• Writing that resistance “uses up” current. A resistor limits the current but does not use it up.
• Connecting the voltmeter in series or the ammeter in parallel.
• Saying “a filament lamp does not obey V = IR”. The equation still works at each point. What changes is R.
• Using the gradient of a curve as the resistance. Use V ÷ I at the point.
• Mixing up the thermistor and the LDR: temperature controls a thermistor, light intensity controls an LDR.
• Describing the lamp’s curve as “resistance decreases”. It increases, because the filament heats.
• Forgetting to convert mA to A, or kΩ to Ω, before using V = IR.
• Drawing a diode graph as a symmetrical line. It must show almost no current in reverse.

Next steps

Work through the practice questions, then use the revision notes to tidy your recall. Tick off progress on the checklist, and check the course hub for other topics.

Official syllabus

OCR GCSE (9-1) Gateway Science Physics A (J249) specification, Version 5.0 (July 2026), for first assessment in 2018, published by OCR.