Practise › Questions › Resistivity and superconductivity
Resistivity and superconductivity questions
Resistance belongs to a particular wire; reshape it and R changes with the geometry. Divide the shape out and what remains is resistivity, the material's own property. Temperature changes that property, and in a few materials it falls to zero below a critical temperature.
18 original questions · 58 marks · the resistivity and superconductivity notes · Electricity
Every question here is written for this library rather than taken from a past paper. Write your answer out before opening a mark scheme: the schemes award marks point by point, and the marks are easier to see when you have something of your own to compare against.
State the equation relating the resistance of a wire to its resistivity, and give the unit of resistivity.
Mark scheme
R = ρL/A, where ρ is the resistivity, L the length and A the cross-sectional area (1). Resistivity has the unit ohm metre, Ω m (1).A copper wire (resistivity 1.7 × 10−8 Ω m) has length 2.0 m and cross-sectional area 1.0 × 10−6 m2. Calculate its resistance.
Mark scheme
R = ρL/A = (1.7 × 10−8 × 2.0)/(1.0 × 10−6) (1)
R = 0.034 Ω (1)State what is meant by superconductivity.
Mark scheme
Below a critical temperature the resistivity of a superconductor falls to zero (1), so it conducts electricity with no resistance and no energy dissipated (1).State how the resistance of an ntc thermistor changes as its temperature rises, and give one practical use of a thermistor.
Mark scheme
The resistance falls (steeply) as the temperature rises (1). Used as a temperature sensor, for example in a thermostat, a car engine monitor or an incubator (1).A uniform wire of resistance 3.2 Ω is cut into two equal lengths. State the resistance of each half.
Mark scheme
1.6 Ω, since R ∝ L and each piece has half the length (1).A wire of length 1.5 m and diameter 0.40 mm has a resistance of 0.50 Ω. Calculate (a) its cross-sectional area and (b) the resistivity of its material.
Mark scheme
(a) A = π(d/2)2 = π × (0.20 × 10−3)2 (1)
A = 1.26 × 10−7 m2 (1)
(b) ρ = RA/L = (0.50 × 1.26 × 10−7)/1.5 (1)
ρ = 4.2 × 10−8 Ω m, to the two significant figures the data carry (1)A wire of resistivity 2.8 × 10−8 Ω m and cross-sectional area 2.0 × 10−6 m2 is to have a resistance of 0.10 Ω. Calculate the length required.
Mark scheme
L = RA/ρ (1)
L = (0.10 × 2.0 × 10−6)/(2.8 × 10−8) (1)
L = 7.14 m (1)A wire's length is doubled and its cross-sectional area is halved. State the factor by which its resistance changes, and explain why.
Mark scheme
Resistance increases by a factor of 4 (1). From R = ρL/A, doubling L doubles R (1), and halving A doubles R again, giving 2 × 2 = 4 times the original resistance (1).Describe qualitatively how the resistance of a metal wire changes as its temperature increases, and why.
A heater manufacturer needs a 1.2 m length of nichrome wire (resistivity 1.1 × 10−6 Ω m) to have a resistance of 15 Ω. Calculate the diameter of wire required.
The mass of a 4.00 m length of copper wire is 2.85 g. The density of copper is 8930 kg m−3 and its resistivity is 1.7 × 10−8 Ω m. Calculate (a) the cross-sectional area of the wire and (b) its resistance.
The main coil of an MRI scanner carries a current of 480 A and is normally superconducting. During a fault the coil warms above its critical temperature and develops a resistance of 0.25 Ω. Calculate the power dissipated in the coil during the fault, and state the power dissipated during normal operation.
Two wires are made of the same material. Wire B has twice the length and twice the diameter of wire A. If wire A has a resistance of 8.0 Ω, calculate the resistance of wire B.
A heating element is made from wire of resistivity 1.1 × 10−6 Ω m, length 5.0 m and cross-sectional area 2.0 × 10−7 m2. Calculate its resistance and its power when connected to a 230 V supply.
Describe what happens to a superconductor at its critical temperature and give one practical use of superconductors.
A student needs a 2.0 m length of wire with a resistance between 4.5 Ω and 5.5 Ω. Four reels are available. Wire W: copper (ρ = 1.7 × 10−8 Ω m), diameter 0.25 mm. Wire X: constantan (ρ = 4.9 × 10−7 Ω m), diameter 0.50 mm. Wire Y: constantan, diameter 0.25 mm. Wire Z: nichrome (ρ = 1.1 × 10−6 Ω m), diameter 0.50 mm. Deduce which wire the student should use.
A metal wire and an ntc thermistor happen to have the same resistance at 20 °C. Both are then warmed to 80 °C. Compare what happens to the resistance of each, explaining both changes in terms of the charge carriers and the lattice.
A student measures the resistance R of several different lengths L of the same wire and plots R against L, obtaining a straight line through the origin with gradient 2.4 Ω m−1. The wire's diameter is 0.20 mm. Determine the resistivity of the wire's material.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
Practise resistivity and superconductivity one question at a time
The player marks nothing for you. It shows one question, waits, then shows the scheme so you can mark yourself, and brings a question back sooner when it went badly.