IGCSE Physics 0625 · Topic 4.2.4

IGCSE Physics Resistance Questions and Worked Solutions

50 topic-wise practice questions on Resistance (Unit 4: Electricity and Magnetism), written to the Cambridge IGCSE Physics 0625 syllabus for 2026–2028, each with a step-by-step worked solution.

50 questions19 Core21 Extended10 Challenge134 marksTextbook §4.2 · pp. 184–208

Questions tagged Core are for all candidates (Papers 1 & 3). Questions tagged Extended are Supplement content (Papers 2 & 4). Questions 41–50 are harder Challenge questions. Try each question first, then tap Show solution to check your working.

Topic guide: Resistance

Resistance opposes the flow of current. It is calculated from the p.d. and current. The resistance of a wire depends on its length and thickness. Different components have characteristic current–voltage graphs.

Key formulas

R = V ÷ I	resistance R (Ω), p.d. V (V), current I (A)	Core
R ∝ L	resistance is directly proportional to length	Extended
R ∝ 1/A	resistance is inversely proportional to cross-sectional area	Extended

Prerequisite knowledge

Current and p.d. (4.2.2, 4.2.3)
Proportion and inverse proportion

Exam tips & common mistakes

Doubling the diameter quadruples the area, so R becomes a quarter
Convert kΩ to Ω and mA to A
Explain the lamp curve using temperature

Key facts from the syllabus (4.2.4)

Determine resistance with an ammeter (series) and voltmeter (parallel); use a variable resistor for several readings
Longer wire → more resistance; thicker wire → less resistance
Extended I–V graph for a fixed resistor is a straight line through the origin (constant R)
Extended filament lamp I–V graph curves — resistance increases as the filament heats up
Extended diode conducts in one direction only; very high resistance in reverse

Textbook: §4.2 Electrical quantities, pp. 184–208

Core[1 mark]

State the equation linking resistance, p.d. and current.

Show solutionHide solution

Method: R = V/I.

R = V ÷ I

Core[2 marks]

A p.d. of 12 V gives a current of 0.50 A. Calculate the resistance.

Show solutionHide solution

Method: R = V ÷ I.

R = 12 ÷ 0.50 = 24.0 Ω

Core[2 marks]

A 15 Ω resistor carries 0.40 A. Calculate the p.d. across it.

Show solutionHide solution

Method: V = IR.

V = 0.40 × 15 = 6.00 V

Core[2 marks]

A 230 V supply is connected to a 46 Ω heater. Calculate the current.

Show solutionHide solution

Method: I = V ÷ R.

I = 230 ÷ 46 = 5.00 A

Core[4 marks]

Describe an experiment to determine the resistance of a wire using an ammeter and a voltmeter.

Show solutionHide solution

Method: Series ammeter, parallel voltmeter, R = V/I.

Connect the wire in series with a cell, switch and ammeter; connect a voltmeter across the wire; record V and I for several settings (using a variable resistor); calculate R = V ÷ I and average

Core[2 marks]

State how the resistance of a metal wire depends on its length and cross-sectional area.

Show solutionHide solution

Method: Longer → more R; thicker → less R.

Longer wire has greater resistance; thicker wire (larger area) has less resistance

Core[2 marks]

A current of 25 mA flows through a 2.0 kΩ resistor. Calculate the p.d.

Show solutionHide solution

Method: Convert units.

V = 0.025 × 2000 = 50.0 V

Core[2 marks]

Explain why connecting wires in a circuit are made thick and from copper.

Show solutionHide solution

Method: Low resistance.

Thick copper wires have very low resistance, so little energy is wasted

Core[2 marks]

A resistor has 9.0 V across it and resistance 300 Ω. Calculate the current in mA.

Show solutionHide solution

Method: I = V/R.

I = 9.0 ÷ 300 = 0.0300 A = 30.0 mA

Core[2 marks]

A lamp draws 0.25 A at 6.0 V. Calculate its resistance.

Show solutionHide solution

Method: R = V/I.

R = 24.0 Ω

Core[2 marks]

A 2.2 kΩ resistor has 11 V across it. Calculate the current in mA.

Show solutionHide solution

Method: I = V/R.

I = 5.00 mA

Core[2 marks]

Calculate the p.d. across a 470 Ω resistor carrying 20 mA.

Show solutionHide solution

Method: V = IR.

V = 9.40 V

Core[2 marks]

State the unit of resistance and its definition in terms of V and A.

Show solutionHide solution

Method: Ω = V/A.

ohm (Ω); 1 Ω = 1 V/A

Core[2 marks]

Explain why a long thin wire has a high resistance.

Show solutionHide solution

Method: Length and area.

Electrons collide more often over a longer path, and a small area gives fewer paths for current

Core[2 marks]

State what happens to the resistance if a wire is replaced by a shorter one of the same material and thickness.

Show solutionHide solution

Method: Decreases.

The resistance decreases

Core[3 marks]

A student records V = 1.5, 3.0, 4.5 V and I = 0.10, 0.20, 0.30 A for a resistor. Calculate the resistance and comment.

Show solutionHide solution

Method: R = V/I.

R = 15.0 Ω each time; resistance is constant

Core[2 marks]

State the purpose of a variable resistor in a resistance experiment.

Show solutionHide solution

Method: Vary current.

To change the current so several readings of V and I can be taken

Core[3 marks]

Describe how to use a voltmeter and ammeter to find the resistance of a lamp at different currents.

Show solutionHide solution

Method: Vary and record.

Connect the lamp with an ammeter in series and voltmeter in parallel; use a variable resistor to change the current; record V and I each time and calculate R = V/I

Core[2 marks]

A resistor has 0 V across it. State the current through it.

Show solutionHide solution

Method: I = V/R.

Zero

Extended[2 marks]

Sketch and describe the current–voltage graph for a resistor of constant resistance.

Show solutionHide solution

Method: Straight line through origin.

A straight line through the origin (current proportional to p.d.)

Extended[3 marks]

Sketch and explain the current–voltage graph for a filament lamp.

Show solutionHide solution

Method: Curve flattening.

A curve whose gradient decreases as V increases: the filament heats up and its resistance increases

Extended[3 marks]

Sketch and explain the current–voltage graph for a diode.

Show solutionHide solution

Method: Current one direction only.

Almost no current in reverse; in the forward direction current rises sharply above about 0.6 V: a diode has very high resistance in reverse

Extended[3 marks]

A wire of length 1.0 m has resistance 4.0 Ω. Calculate the resistance of 2.5 m of the same wire.

Show solutionHide solution

Method: R ∝ L.

R = 4.0 × 2.5 = 10.0 Ω

Extended[3 marks]

A wire has resistance 12 Ω. Calculate the resistance of a wire of the same material and length but double the cross-sectional area.

Show solutionHide solution

Method: R ∝ 1/A.

R = 12 ÷ 2 = 6.00 Ω

Extended[3 marks]

A wire has resistance 8.0 Ω. A second wire of the same material is twice as long and has three times the cross-sectional area. Calculate its resistance.

Show solutionHide solution

Method: R ∝ L/A.

R = 8.0 × 2 ÷ 3 = 5.33 Ω

Extended[3 marks]

A wire's diameter is halved, with length unchanged. State the factor by which its resistance changes.

Show solutionHide solution

Method: Area ∝ d², so area becomes ¼.

Resistance increases by a factor of 4

Extended[2 marks]

Explain why the resistance of a filament lamp increases as the current increases.

Show solutionHide solution

Method: Temperature rises.

The filament gets hotter; its metal ions vibrate more, so electrons collide more often

Extended[2 marks]

Explain the purpose of a diode in a circuit.

Show solutionHide solution

Method: One-way.

It allows current in one direction only

Extended[3 marks]

For a filament lamp, V = 2.0 V gives I = 0.20 A and V = 6.0 V gives I = 0.30 A. Calculate the resistance at each p.d. and comment.

Show solutionHide solution

Method: R = V/I.

R = 10.0 Ω and 20.0 Ω; resistance increases with p.d. (filament heats up)

Extended[2 marks]

State the reading on the ammeter when a diode is connected in reverse bias in a series circuit.

Show solutionHide solution

Method: Very high resistance.

Approximately zero

Extended[2 marks]

Describe the current–voltage graph for a resistor when the p.d. is reversed.

Show solutionHide solution

Method: Straight line through origin into third quadrant.

A straight line through the origin, continuing into negative values

Extended[2 marks]

Describe what happens to the gradient of the I–V graph of a filament lamp as V increases.

Show solutionHide solution

Method: Decreases.

The gradient decreases (resistance increases)

Extended[2 marks]

State the approximate forward p.d. at which a silicon diode begins to conduct.

Show solutionHide solution

Method: ~0.6 V.

About 0.6–0.7 V

Extended[3 marks]

A wire of length 50 cm has resistance 2.0 Ω. Calculate the resistance of 1.5 m of the same wire.

Show solutionHide solution

Method: R ∝ L.

R = 6.00 Ω

Extended[3 marks]

A wire has resistance 9.0 Ω. A wire of the same material and length has three times the cross-sectional area. Calculate its resistance.

Show solutionHide solution

Method: R ∝ 1/A.

R = 3.00 Ω

Extended[3 marks]

A wire of resistance 4.0 Ω is stretched to twice its length, halving its area. Calculate the new resistance.

Show solutionHide solution

Method: R ∝ L/A.

R = 4.0 × 2 × 2 = 16.0 Ω

Extended[3 marks]

Wire A: length 2.0 m, area 1.0 mm², R = 3.4 Ω. Calculate the resistance of wire B of the same metal: length 1.0 m, area 0.50 mm².

Show solutionHide solution

Method: R ∝ L/A.

R = 3.4 × 0.5 × 2 = 3.40 Ω

Extended[2 marks]

Explain why a filament lamp does not obey Ohm's law but a resistor at constant temperature does.

Show solutionHide solution

Method: Temperature changes.

The filament's temperature, and so its resistance, rises with current

Extended[2 marks]

Explain how a diode can protect a circuit if a battery is connected the wrong way round.

Show solutionHide solution

Method: Blocks reverse.

It has very high resistance in reverse, preventing current

Extended[3 marks]

A filament lamp has resistance 4.0 Ω cold and 48 Ω at its working current of 0.25 A. Calculate the working p.d. and explain the difference.

Show solutionHide solution

Method: V = IR.

V = 12.0 V; resistance rises because the filament heats up

Challenge questions

Harder, multi-step questions at the top end of the exam. Attempt these once you are confident with the questions above.

ChallengeCore[4 marks]

Describe how to use an ammeter, voltmeter and variable resistor to find the resistance of a wire, including how to obtain a reliable value.

Show solutionHide solution

Method: Several readings.

Wire in series with ammeter, voltmeter across wire; vary current with variable resistor; record several V and I values; plot V against I and find the gradient (= R)

ChallengeCore[4 marks]

A wire of length 0.50 m has resistance 1.2 Ω. Predict the resistance of 2.0 m of the same wire and of a 0.50 m wire with twice the cross-sectional area.

Show solutionHide solution

Method: Qualitative then scaled.

2.0 m: 4.8 Ω; double area: 0.60 Ω

ChallengeCore[3 marks]

Explain why the resistance of a thin wire is greater than that of a thick wire of the same material and length.

Show solutionHide solution

Method: Fewer paths.

A thin wire has a smaller cross-section, so fewer electrons can pass at once; collisions with ions impede them more

ChallengeExtended[5 marks]

A filament lamp: V = 1.0, 2.0, 4.0, 6.0 V; I = 0.10, 0.17, 0.25, 0.30 A. Calculate the resistance at each p.d. and explain the trend.

Show solutionHide solution

Method: R = V/I.

10.0, 11.8, 16.0, 20.0 Ω; resistance increases as the filament gets hotter

ChallengeExtended[4 marks]

A silicon diode is connected in series with a 1.0 kΩ resistor across 5.0 V in forward bias. The diode drops 0.7 V. Calculate the current. State the current if the diode is reversed.

Show solutionHide solution

Method: Remaining p.d. across resistor.

I = 4.3 ÷ 1000 = 4.30 mA; reversed: almost zero

ChallengeExtended[4 marks]

Wire A: length L, diameter d, resistance 6.0 Ω. Wire B (same metal): length 2L, diameter 2d. Calculate the resistance of B.

Show solutionHide solution

Method: Area ∝ d².

R = 6.0 × 2 ÷ 4 = 3.00 Ω

ChallengeExtended[4 marks]

A 10 m length of copper wire has resistance 0.50 Ω. Calculate the length of the same wire needed for 2.0 Ω, and the resistance if the 10 m wire is folded in half to make a doubled 5 m wire.

Show solutionHide solution

Method: R ∝ L/A.

40.0 m; folded: L halves, A doubles, R = 0.125 Ω

ChallengeExtended[3 marks]

Sketch (describe) and compare the I–V graphs for a fixed resistor and a filament lamp, explaining the difference.

Show solutionHide solution

Method: Straight vs curve.

Resistor: straight line through origin (constant R); lamp: curve whose gradient decreases as V increases, because the filament heats and R increases

ChallengeExtended[4 marks]

A thermistor in a circuit has V = 6.0 V across it and I = 2.0 mA at 20 °C; at 60 °C, I = 12 mA. Calculate its resistance at both temperatures and identify the type.

Show solutionHide solution

Method: R = V/I.

3000 Ω and 500 Ω; resistance falls with temperature (NTC)

ChallengeExtended[4 marks]

Explain why a diode is described as having a very high resistance in one direction, using its I–V graph.

Show solutionHide solution

Method: Reverse region.

In reverse bias the current is almost zero for any p.d. (very high resistance); in forward bias current rises steeply above about 0.6 V

All IGCSE Physics topics ← 4.2.3 Electromotive Force and Potential Difference 4.2.5 Electrical Energy and Electrical Power →

Book a free trial class

Tell us a little about your requirement.