AQA A-Level Physics: Electricity

A student investigates how the current through two components varies with the potential difference across them. The two components are a fixed metallic resistor at constant temperature and a filament lamp. The student plots a graph of current $I$I (y-axis) against potential difference $V$V (x-axis) for each.

The metallic resistor gives a straight line through the origin. The filament lamp gives a curve that passes through the origin but bends towards the $V$V-axis as the potential difference increases.

Explain the shape of each I-V characteristic. Your answer should explain why the metallic resistor obeys Ohm's law while the filament lamp does not, and should refer to what happens to the resistance of the filament and the reason for it.

(6 marks)

A cell of EMF $\varepsilon$ε and internal resistance $r$r is connected to a variable resistor. As the resistance is changed, the terminal potential difference $V$V across the cell and the current $I$I drawn from it are measured. The results are shown below.

Current $I$I / A	0.40	0.80	1.20	1.60	2.00
Terminal pd $V$V / V	1.30	1.10	0.90	0.70	0.50

The measurements obey the equation $V = \varepsilon - Ir$V=ε−Ir.

(a) State how the EMF and the internal resistance can be found from a graph of $V$V against $I$I. (2 marks)

(b) Use the first and last data points to calculate the EMF and the internal resistance of the cell. (4 marks)

A battery of EMF $12 \ \text{V}$12 V and negligible internal resistance is connected to a network of three resistors. A $6.0 \ \Omega$6.0 Ω resistor and a $3.0 \ \Omega$3.0 Ω resistor are connected in parallel with each other. This parallel combination is connected in series with a $4.0 \ \Omega$4.0 Ω resistor, and the whole arrangement is connected across the battery.

Resistor	Resistance / Ω
R₁ (parallel branch)	6.0
R₂ (parallel branch)	3.0
R₃ (in series with the pair)	4.0

(a) Calculate the total resistance of the network. (2 marks)

(b) Calculate the current drawn from the battery. (1 mark)

(c) Calculate the current through the $6.0 \ \Omega$6.0 Ω resistor. (2 marks)

An engineer is designing the heating element for an electric toaster. The element is a length of resistance wire. A test sample of the wire has the following measured properties.

Quantity	Value
Length $l$l	2.0 m
Diameter $d$d	0.40 mm
Resistance $R$R	17.5 Ω

(a) Show that the cross-sectional area of the wire is approximately $1.3 \times 10^{-7} \ \text{m}^2$1.3×10−7 m2. (1 mark)

(b) Calculate the resistivity of the wire material. Give your answer with an appropriate unit. (3 marks)

(c) For the final design the engineer uses wire of the same material and the same diameter but twice the length. State the resistance of this element. (1 mark)

A potential-divider circuit is used to switch on a cooling fan when a greenhouse becomes too hot. A supply of EMF $12 \ \text{V}$12 V (negligible internal resistance) is connected across a negative temperature coefficient (NTC) thermistor in series with a fixed $2.0 \ \text{k}\Omega$2.0 kΩ resistor. The output voltage $V_{\text{out}}$Vout​ that drives the fan circuit is taken across the fixed $2.0 \ \text{k}\Omega$2.0 kΩ resistor.

The resistance of the thermistor is $10.0 \ \text{k}\Omega$10.0 kΩ when the greenhouse is cold and $0.50 \ \text{k}\Omega$0.50 kΩ when it is hot.

(a) Calculate $V_{\text{out}}$Vout​ when the greenhouse is cold. (2 marks)

(b) Calculate $V_{\text{out}}$Vout​ when the greenhouse is hot, and hence state how the output voltage changes as the temperature rises. (2 marks)

Kirchhoff's two circuit laws are each a statement of a conservation principle.

State Kirchhoff's first law and Kirchhoff's second law, and for each law name the physical quantity that is conserved. (3 marks)