OCR A-Level Physics: Electricity and Circuits

A student investigates the current-voltage ($I$I-$V$V) characteristics of two components: a fixed metal-film resistor kept at a steady temperature, and a filament lamp. The resistor gives a straight line through the origin, whereas the filament lamp gives a curve that bends towards the voltage axis as the voltage rises.

Explain, in terms of the behaviour of the charge carriers and the resistance of each component, why the resistor obeys Ohm's law but the filament lamp does not. Your answer should describe the shape of each characteristic and account for the change in resistance of the filament as the voltage is increased.

(6 marks)

A technician determines the resistivity of the alloy constantan by measuring the resistance of a uniform wire sample. The measured values are:

Quantity	Value
Length of wire, $L$L	1.50 m
Diameter of wire, $d$d	0.40 mm
Resistance of wire, $R$R	5.85 Ω

(a) Calculate the cross-sectional area of the wire, in $\text{m}^2$m2. (3 marks)

(b) Hence calculate the resistivity of constantan, giving your answer in $\Omega \ \text{m}$Ω m to an appropriate number of significant figures. (3 marks)

(Use $R = \dfrac{\rho L}{A}$R=AρL​.)

(6 marks)

A student records the current through a component for a range of potential differences across it:

Voltage / V	0.50	1.00	1.50	2.00	2.50	3.00
Current / mA	25.0	50.0	74.5	92.0	104.0	112.5

(a) Use the data to determine whether the component is ohmic over the whole range. Justify your answer with a calculation. (2 marks)

(b) Calculate the resistance of the component at $V = 1.00 \ \text{V}$V=1.00 V and at $V = 3.00 \ \text{V}$V=3.00 V. (2 marks)

(c) State, with a reason, what your results suggest the component is. (1 mark)

(5 marks)

A robotics club tests a battery pack that has an electromotive force (EMF) $\varepsilon$ε and internal resistance $r$r. They connect it to two different load resistors and record the terminal pd $V$V and current $I$I in each case:

• With a $4.0 \ \Omega$4.0 Ω load: $I = 1.20 \ \text{A}$I=1.20 A and $V = 6.00 \ \text{V}$V=6.00 V.
• With a $2.0 \ \Omega$2.0 Ω load: $I = 2.00 \ \text{A}$I=2.00 A and $V = 5.60 \ \text{V}$V=5.60 V.

The terminal pd, current and EMF are related by $\varepsilon = V + Ir$ε=V+Ir.

(a) Use the two sets of readings to determine the internal resistance $r$r of the battery pack. (3 marks)

(b) Hence determine the EMF $\varepsilon$ε of the battery pack. (2 marks)

(5 marks)

The heating element of an electric kettle is a coil of resistance 18 Ω connected to the 230 V mains supply.

(a) Calculate the power dissipated by the element. (2 marks)

(b) The kettle is run for 4.0 minutes. If electrical energy costs 28 p per kWh, calculate the cost of running the kettle for this time. (2 marks)

(4 marks)

The transport of charge in a metal can be described by the equation $I = nAve$I=nAve, where $n$n is the number of free electrons per unit volume, $A$A is the cross-sectional area, $v$v is the mean drift velocity and $e$e is the electronic charge.

(a) Define the electric current in terms of charge. (1 mark)

(b) A copper wire of cross-sectional area $1.0 \times 10^{-6} \ \text{m}^2$1.0×10−6 m2 carries a current of $3.2 \ \text{A}$3.2 A. For copper, $n = 8.5 \times 10^{28} \ \text{m}^{-3}$n=8.5×1028 m−3 and $e = 1.6 \times 10^{-19} \ \text{C}$e=1.6×10−19 C. Calculate the mean drift velocity of the electrons, with its unit. (2 marks)

(3 marks)