Resistance and resistivity
9.3What the syllabus asks of you
- define resistance
- recall and use V = IR
- sketch the I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp
- explain that the resistance of a filament lamp increases as current increases because its temperature increases
- state Ohm’s law
- recall and use R = ρL / A
- understand that the resistance of a light-dependent resistor (LDR) decreases as the light intensity increases
- understand that the resistance of a thermistor decreases as the temperature increases (it will be assumed that thermistors have a negative temperature coefficient)
Read the notes first
Chapter 9: Resistance and resistivity
Drill this topic
Every question on Resistance and resistivity, untimed, marked as you go.
Make a worksheet
Choose the years and how many questions, then print it with the answers on separate pages.
104 questions
1May / June 2026 · Paper 11 · Q32Show mark scheme →
Agraph A: R decreasing linearly with A
Bgraph B: R decreasing as inverse of A
Cgraph C: R increasing linearly with A
Dgraph D: R increasing non-linearly with A
Mark scheme
2May / June 2026 · Paper 11 · Q37Show mark scheme →
Avoltmeter reading decreases, ammeter reading decreases
Bvoltmeter reading decreases, ammeter reading increases
Cvoltmeter reading increases, ammeter reading decreases
Dvoltmeter reading increases, ammeter reading increases
Mark scheme
3May / June 2026 · Paper 12 · Q32Show mark scheme →
Afilament lamp — increase in electric current
Blight-dependent resistor (LDR) — increase in light intensity
Csemiconductor diode — increase in electric current
Dthermistor — increase in temperature
Mark scheme
4May / June 2026 · Paper 12 · Q33Show mark scheme →
AR
B2R
C4R
D16R
Mark scheme
5May / June 2026 · Paper 13 · Q33Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
Mark scheme
6May / June 2026 · Paper 14 · Q34Show mark scheme →
AGraph A: R increases with light intensity (curve rising from origin)
BGraph B: R decreases with light intensity (curve falling)
CGraph C: R decreases linearly with light intensity
DGraph D: R constant with light intensity
Mark scheme
7Oct / Nov 2025 · Paper 11 · Q33Show mark scheme →
Afilament lamp P, semiconductor diode R
Bfilament lamp P, semiconductor diode S
Cfilament lamp Q, semiconductor diode R
Dfilament lamp Q, semiconductor diode S
Mark scheme
8Oct / Nov 2025 · Paper 11 · Q36Show mark scheme →
A2/5
B2/3
C3/2
D5/2
Mark scheme
9Oct / Nov 2025 · Paper 12 · Q33Show mark scheme →
Aresistivity ½ρ, cross-sectional area ½A
Bresistivity ½ρ, cross-sectional area A
Cresistivity ρ, cross-sectional area ½A
Dresistivity 2ρ, cross-sectional area A
Mark scheme
10Oct / Nov 2025 · Paper 13 · Q33Show mark scheme →
Afilament lamp P; semiconductor diode R
Bfilament lamp P; semiconductor diode S
Cfilament lamp Q; semiconductor diode R
Dfilament lamp Q; semiconductor diode S
Mark scheme
11Oct / Nov 2025 · Paper 13 · Q36Show mark scheme →
A2/5
B2/3
C3/2
D5/2
Mark scheme
12Oct / Nov 2025 · Paper 14 · Q32Show mark scheme →
Afilament lamp
Bmetallic conductor at constant temperature
Cresistor of fixed resistance
Dsemiconductor diode
Mark scheme
13Oct / Nov 2025 · Paper 14 · Q34Show mark scheme →
A\frac{1}{4}P
B\frac{1}{2}P
C2P
D4P
Mark scheme
14May / June 2025 · Paper 11 · Q32Show mark scheme →
Acurrent divided by potential difference
Bcurrent multiplied by potential difference
Cpotential difference divided by current
Dresistivity multiplied by length
Mark scheme
15May / June 2025 · Paper 11 · Q33Show mark scheme →
Aa filament lamp
Ba metallic conductor at constant temperature
Ca resistor
Da semiconductor diode
Mark scheme
16May / June 2025 · Paper 12 · Q32Show mark scheme →
AIt is directly proportional to the length of the wire.
BIt is inversely proportional to the length of the wire.
CIt is directly proportional to the diameter of the wire.
DIt is inversely proportional to the diameter of the wire.
Mark scheme
17May / June 2025 · Paper 12 · Q33Show mark scheme →
A1, 2 and 3
B1 and 2 only
C1 and 3 only
D1 only
Mark scheme
18May / June 2025 · Paper 13 · Q34Show mark scheme →
A1.76 × 10⁻⁴ m
B3.52 × 10⁻⁴ m
C1.26 × 10⁻³ m
D2.51 × 10⁻³ m
Mark scheme
19May / June 2025 · Paper 14 · Q31Show mark scheme →
Aa filament lamp as the potential difference (p.d.) across it increases
Ba light-dependent resistor (LDR) as the intensity of the light incident on it increases
Ca metallic conductor at constant temperature as the current through it increases
Da thermistor as its temperature increases
Mark scheme
20May / June 2025 · Paper 14 · Q32Show mark scheme →
A3.6 × 10⁻¹⁸ Ω
B5.8 × 10⁻¹³ Ω
C9.2 × 10⁻⁴ Ω
D6.8 × 10⁻³ Ω
Mark scheme
21Feb / March 2025 · Paper 12 · Q31Show mark scheme →
A5.7 × 10⁻⁵ m
B1.0 × 10⁻⁴ m
C4.0 × 10⁻⁴ m
D7.1 × 10⁻⁴ m
Mark scheme
22Feb / March 2025 · Paper 12 · Q32Show mark scheme →
AGraph A: P increases with temperature / °C (upward curve)
BGraph B: P decreases with temperature / °C (downward curve)
CGraph C: P constant with temperature / °C (horizontal line)
DGraph D: P decreases linearly with temperature / °C (straight line)
Mark scheme
23Oct / Nov 2024 · Paper 12 · Q33Show mark scheme →
AGraph A: I against V, curve starting at origin with decreasing gradient (concave down)
BGraph B: I against V, straight line through origin
CGraph C: I against V, curve starting high at V=0 and decreasing (concave up)
DGraph D: I against V, curve starting at origin with increasing gradient (concave up)
Mark scheme
24Oct / Nov 2024 · Paper 13 · Q33Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
Mark scheme
25May / June 2024 · Paper 11 · Q31Show mark scheme →
AΩ m⁻²
BΩ m⁻¹
CΩ
DΩ m
Mark scheme
26May / June 2024 · Paper 12 · Q31Show mark scheme →
A
B
C
D
Mark scheme
27May / June 2024 · Paper 13 · Q31Show mark scheme →
AThe brightness of the lamp decreases.
BThe potential difference across the filament decreases.
CThe resistance of the filament decreases.
DThe temperature of the filament increases.
Mark scheme
28May / June 2024 · Paper 13 · Q33Show mark scheme →
AρV^{1/3}
BρV^{2/3}
Cρ / V^{1/3}
Dρ / V^{2/3}
Mark scheme
29Oct / Nov 2023 · Paper 11 · Q32Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
Mark scheme
30Oct / Nov 2023 · Paper 11 · Q33Show mark scheme →
A0.033 Ω m
B0.10 Ω m
C0.42 Ω m
D5.2 Ω m
Mark scheme
31Oct / Nov 2023 · Paper 12 · Q32Show mark scheme →
AIt is directly proportional to l and inversely proportional to d.
BIt is directly proportional to l and inversely proportional to d².
CIt is inversely proportional to l and directly proportional to d.
DIt is inversely proportional to l and directly proportional to d².
Mark scheme
32Oct / Nov 2023 · Paper 13 · Q32Show mark scheme →
AThe charge of each charge carrier increases.
BThe potential difference across the filament decreases.
CThe power dissipated by the filament decreases.
DThe temperature of the filament increases.
Mark scheme
33Oct / Nov 2023 · Paper 13 · Q33Show mark scheme →
Aincreases, 60
Bdecreases, 60
Cincreases, 100
Ddecreases, 100
Mark scheme
34May / June 2023 · Paper 11 · Q32Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
Mark scheme
35May / June 2023 · Paper 11 · Q33Show mark scheme →
A0.012 Ω
B0.024 Ω
C0.19 Ω
D0.22 Ω
Mark scheme
36May / June 2023 · Paper 12 · Q32Show mark scheme →
A4A / (33RL)
B12A / (RL)
C4AR / L
D12AR / L
Mark scheme
37May / June 2023 · Paper 12 · Q33Show mark scheme →
Aresistance of LDR increases; resistance of thermistor increases
Bresistance of LDR increases; resistance of thermistor decreases
Cresistance of LDR decreases; resistance of thermistor increases
Dresistance of LDR decreases; resistance of thermistor decreases
Mark scheme
38May / June 2023 · Paper 13 · Q32Show mark scheme →
A1.2 × 10⁻⁷ m²
B1.7 × 10⁻⁷ m²
C1.1 × 10⁻⁶ m²
D1.3 × 10⁻⁵ m²
Mark scheme
39May / June 2023 · Paper 13 · Q33Show mark scheme →
AGraph A: I against T, curve starting at a constant value then decreasing
BGraph B: I against T, curve increasing from a low value
CGraph C: I against T, straight line decreasing
DGraph D: I against T, curve decreasing steeply from a high value
Mark scheme
40Feb / March 2023 · Paper 12 · Q32Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
Mark scheme
41Feb / March 2023 · Paper 12 · Q33Show mark scheme →
A0.41$d$
B1.6$d$
C2.7$d$
D7.1$d$
Mark scheme
42Oct / Nov 2022 · Paper 11 · Q2Show mark scheme →
A150 mA, 0.24 kΩ
B15 mA, 2.4 kΩ
C1.5 mA, 0.24 MΩ
D15 μA, 240 kΩ
Mark scheme
43Oct / Nov 2022 · Paper 11 · Q33Show mark scheme →
A√2
B2
C2√2
D4
Mark scheme
44Oct / Nov 2022 · Paper 12 · Q33Show mark scheme →
AThe resistance of the lamp decreases because the temperature decreases.
BThe resistance of the lamp decreases because the temperature increases.
CThe resistance of the lamp increases because the temperature decreases.
DThe resistance of the lamp increases because the temperature increases.
Mark scheme
45Oct / Nov 2022 · Paper 12 · Q34Show mark scheme →
A1.06R
B1.13R
C1.20R
D1.28R
Mark scheme
46Oct / Nov 2022 · Paper 13 · Q32Show mark scheme →
Afilament lamp
Bmetallic conductor at constant temperature
Cresistor of fixed resistance
Dsemiconductor diode
Mark scheme
47Oct / Nov 2022 · Paper 13 · Q33Show mark scheme →
A\frac{1}{8}
B\frac{1}{4}
C\frac{1}{2}
D\frac{2}{1}
Mark scheme
48May / June 2022 · Paper 11 · Q33Show mark scheme →
AAbove a certain positive potential difference the diode obeys Ohm's law.
BCurrent is directly proportional to potential difference when the current in the diode is in one direction.
CThe diode has zero resistance when the current in the diode is in one direction.
DThe resistance of the diode depends upon the potential difference across it.
Mark scheme
49May / June 2022 · Paper 11 · Q34Show mark scheme →
A10 Ω
B30 Ω
C90 Ω
D270 Ω
Mark scheme
50May / June 2022 · Paper 12 · Q33Show mark scheme →
ALDR increases, thermistor increases
BLDR increases, thermistor decreases
CLDR decreases, thermistor increases
DLDR decreases, thermistor decreases
Mark scheme
51May / June 2022 · Paper 12 · Q34Show mark scheme →
A\frac{R}{16}
B\frac{R}{8}
C\frac{R}{2}
DR
Mark scheme
52May / June 2022 · Paper 13 · Q34Show mark scheme →
A0.081 Ω
B12 Ω
C15 Ω
D18 Ω
Mark scheme
53May / June 2022 · Paper 13 · Q35Show mark scheme →
AGraph A: R constant, horizontal line
BGraph B: R proportional to L, straight line through origin
CGraph C: R increases with L, curve with decreasing gradient
DGraph D: R increases with L, curve with increasing gradient
Mark scheme
54Feb / March 2022 · Paper 12 · Q32Show mark scheme →
A1.2 × 10⁻⁷ Ω m
B1.6 × 10⁻⁷ Ω m
C4.9 × 10⁻⁷ Ω m
D2.0 × 10⁻⁶ Ω m
Mark scheme
55Oct / Nov 2021 · Paper 11 · Q34Show mark scheme →
AFor a current of 0.5 A, the power dissipated in Q is double that in P.
BFor a current of 1.9 A, the resistance of Q is approximately half that of P.
CThe resistance of Q increases as the current in it increases.
DP is a fixed resistor and Q is a filament lamp.
Mark scheme
56Oct / Nov 2021 · Paper 11 · Q35Show mark scheme →
A$\dfrac{1}{4}$
B$\dfrac{1}{2}$
C2
D4
Mark scheme
57Oct / Nov 2021 · Paper 12 · Q35Show mark scheme →
Ametal wire at constant temperature: X; semiconductor diode: Z; filament lamp: Y
Bmetal wire at constant temperature: Y; semiconductor diode: X; filament lamp: Z
Cmetal wire at constant temperature: Y; semiconductor diode: Z; filament lamp: X
Dmetal wire at constant temperature: Z; semiconductor diode: X; filament lamp: Y
Mark scheme
58Oct / Nov 2021 · Paper 13 · Q35Show mark scheme →
AR/8
BR/2
CR
D8R
Mark scheme
59May / June 2021 · Paper 11 · Q34Show mark scheme →
Aan increase in the length of the wire
Ban increase in the radius of the wire
Can increase in the resistance of the wire
Dan increase in the resistivity of the wire
Mark scheme
60May / June 2021 · Paper 12 · Q34Show mark scheme →
Ametallic conductor at constant temperature: X; semiconductor diode: Z; filament lamp: Y
Bmetallic conductor at constant temperature: Y; semiconductor diode: X; filament lamp: Z
Cmetallic conductor at constant temperature: Y; semiconductor diode: Z; filament lamp: X
Dmetallic conductor at constant temperature: Z; semiconductor diode: Y; filament lamp: X
Mark scheme
61May / June 2021 · Paper 12 · Q35Show mark scheme →
A1.20 m
B4.80 m
C19.0 m
D76.0 m
Mark scheme
62Feb / March 2021 · Paper 12 · Q34Show mark scheme →
A30 Ω
B120 Ω
C150 Ω
D180 Ω
Mark scheme
63Feb / March 2021 · Paper 12 · Q35Show mark scheme →
A0.0045 V
B0.11 V
C0.45 V
D3.2 V
Mark scheme
64Oct / Nov 2020 · Paper 11 · Q34Show mark scheme →
A10.6 m
B21.2 m
C29.4 m
D58.8 m
Mark scheme
65Oct / Nov 2020 · Paper 12 · Q35Show mark scheme →
A0.071 Ω
B4.2 Ω
C11 Ω
D14 Ω
Mark scheme
66Oct / Nov 2020 · Paper 13 · Q35Show mark scheme →
A1.6 Ω
B2.0 Ω
C10 Ω
D40 Ω
Mark scheme
67May / June 2020 · Paper 11 · Q34Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
Mark scheme
68May / June 2020 · Paper 11 · Q35Show mark scheme →
AR
B2R
C4R
D8R
Mark scheme
69May / June 2020 · Paper 12 · Q35Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
Mark scheme
70May / June 2020 · Paper 13 · Q36Show mark scheme →
AR/4
BR/2
CR
D2R
Mark scheme
71Feb / March 2020 · Paper 12 · Q34Show mark scheme →
AResistance is inversely proportional to both the length and the cross-sectional area.
BResistance is inversely proportional to the length and directly proportional to the cross-sectional area.
CResistance is proportional to both the length and the cross-sectional area.
DResistance is proportional to the length and inversely proportional to the cross-sectional area.
Mark scheme
72Oct / Nov 2019 · Paper 11 · Q33Show mark scheme →
AGraph A: R increases linearly with V from a non-zero intercept
BGraph B: R increases with V from zero, curve concave down
CGraph C: R constant with V
DGraph D: R decreases with V from a high value, curve concave up
Mark scheme
73Oct / Nov 2019 · Paper 13 · Q35Show mark scheme →
Aa filament lamp and a fixed resistor in parallel
Ba filament lamp and a fixed resistor in series
Ca semiconductor diode and a filament lamp in parallel
Da semiconductor diode and a filament lamp in series
Mark scheme
74May / June 2019 · Paper 11 · Q34Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
Mark scheme
75May / June 2019 · Paper 12 · Q34Show mark scheme →
Across-sectional area A, length 2L, temperature 2T
Bcross-sectional area A, length L, temperature T
Ccross-sectional area 2A, length 2L, temperature 2T
Dcross-sectional area 2A, length L, temperature T
Mark scheme
76May / June 2019 · Paper 13 · Q33Show mark scheme →
AG × A
BG / A
CA / G
DG × A²
Mark scheme
77Feb / March 2019 · Paper 12 · Q34Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
Mark scheme
78Feb / March 2019 · Paper 12 · Q35Show mark scheme →
A0.050 m
B0.20 m
C5.0 m
D20 m
Mark scheme
79Oct / Nov 2018 · Paper 11 · Q35Show mark scheme →
AIt is maximum between the faces labelled P.
BIt is maximum between the faces labelled Q.
CIt is maximum between the faces labelled R.
DIt is the same, whichever pair of faces is used.
Mark scheme
80Oct / Nov 2018 · Paper 12 · Q35Show mark scheme →
Aradius r/2, length L/2
Bradius r/√2, length L/2
Cradius r√2, length 2L
Dradius 2r, length 2L
Mark scheme
81Oct / Nov 2018 · Paper 13 · Q34Show mark scheme →
A3.6 × 10⁻¹⁸ Ω
B5.8 × 10⁻¹³ Ω
C9.2 × 10⁻⁴ Ω
D6.8 × 10⁻³ Ω
Mark scheme
82May / June 2018 · Paper 11 · Q4Show mark scheme →
A0 20 40 60 80 100 °C
B0 20 40 60 80 100 °C
C100 80 60 40 20 0 °C
D100 80 60 40 20 0 °C
Mark scheme
83May / June 2018 · Paper 11 · Q32Show mark scheme →
AR/2
BR
C2R
D4R
Mark scheme
84May / June 2018 · Paper 11 · Q37Show mark scheme →
A11.2 V
B16.0 V
C18.4 V
D20.8 V
Mark scheme
85May / June 2018 · Paper 12 · Q33Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
Mark scheme
86May / June 2018 · Paper 13 · Q32Show mark scheme →
Aa filament lamp
Ba metallic conductor at constant temperature
Ca resistor
Da semiconductor diode
Mark scheme
87May / June 2018 · Paper 13 · Q33Show mark scheme →
A0.016 Ω
B0.031 Ω
C33 Ω
D64 Ω
Mark scheme
88Feb / March 2018 · Paper 12 · Q34Show mark scheme →
A1.20 m
B4.80 m
C19.0 m
D76.8 m
Mark scheme
89Oct / Nov 2017 · Paper 11 · Q35Show mark scheme →
A1
B4
C8
D16
Mark scheme
90Oct / Nov 2017 · Paper 12 · Q35Show mark scheme →
AGraph A: V against I, straight line through origin
BGraph B: V against I, curve with increasing gradient
CGraph C: I against V, curve with increasing gradient
DGraph D: I against V, straight line through origin
Mark scheme
91May / June 2017 · Paper 11 · Q34Show mark scheme →
Afilament lamp
Bmetallic conductor at constant temperature
Cresistor of fixed resistance
Dsemiconductor diode
Mark scheme
92May / June 2017 · Paper 12 · Q34Show mark scheme →
A0.17 mm
B0.33 mm
C0.57 mm
D1.0 mm
Mark scheme
93May / June 2017 · Paper 13 · Q33Show mark scheme →
A9R
B3R
C\frac{R}{3}
D\frac{R}{9}
Mark scheme
94Feb / March 2017 · Paper 12 · Q34Show mark scheme →
A\frac{4N\rho D}{d^2}
B\frac{4N\rho d}{D^2}
C\frac{8N\rho D}{d^2}
D\frac{8N\rho d}{D^2}
Mark scheme
95Oct / Nov 2016 · Paper 11 · Q35Show mark scheme →
A10–13 Ω m
B10–8 Ω m
C10–3 Ω m
D102 Ω m
Mark scheme
96Oct / Nov 2016 · Paper 12 · Q35Show mark scheme →
Ametallic conductor at constant temperature: X; semiconductor diode: Z; filament lamp: Y
Bmetallic conductor at constant temperature: Y; semiconductor diode: X; filament lamp: Z
Cmetallic conductor at constant temperature: Y; semiconductor diode: Z; filament lamp: X
Dmetallic conductor at constant temperature: Z; semiconductor diode: Y; filament lamp: X
Mark scheme
97Oct / Nov 2016 · Paper 13 · Q35Show mark scheme →
A10–13 Ω m
B10–8 Ω m
C10–3 Ω m
D102 Ω m
Mark scheme
98May / June 2016 · Paper 11 · Q31Show mark scheme →
A$\dfrac{1}{4}$
B$\dfrac{1}{2}$
C2
D4
Mark scheme
99May / June 2016 · Paper 11 · Q33Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
Mark scheme
100May / June 2016 · Paper 12 · Q32Show mark scheme →
AGraph A: I-V curve rising with decreasing gradient (concave down)
BGraph B: straight line through origin
CGraph C: curve decreasing from high I at low V
DGraph D: curve rising with increasing gradient (concave up)
Mark scheme
101May / June 2016 · Paper 12 · Q34Show mark scheme →
Aenergy = (current)² × resistance × time
Bpotential difference = current × resistance
Cpower = (current)² × resistance
Dresistivity = resistance × area ÷ length
Mark scheme
102May / June 2016 · Paper 13 · Q32Show mark scheme →
AG × A
BG / A
CA / G
DG × A^2
Mark scheme
103May / June 2016 · Paper 13 · Q34Show mark scheme →
Afilament lamp: P; semiconductor diode: R
Bfilament lamp: P; semiconductor diode: S
Cfilament lamp: Q; semiconductor diode: R
Dfilament lamp: Q; semiconductor diode: S
Mark scheme
104Feb / March 2016 · Paper 12 · Q32Show mark scheme →
Ap.d., current, area, length
Bp.d., current, diameter, length
Cresistance, area, length
Dresistance, length, radius
Mark scheme