Edexcel A-Level Physics: Electric Circuits

The current-voltage ($I$I-$V$V) characteristic of a filament lamp is obtained by varying the potential difference across the lamp from zero and recording the current. The resulting graph is a smooth curve through the origin that bends towards the voltage axis as the p.d. increases (the gradient decreases at higher p.d.). The same measurement for a fixed metal resistor at constant temperature gives a straight line through the origin.

Explain, in terms of the behaviour of the charge carriers and the lattice, why the $I$I-$V$V characteristic of the filament lamp has this shape, and why this means the lamp does not obey Ohm's law while the fixed resistor does. In your answer refer to how the resistance of the filament changes and why.

(6 marks)

A cell of electromotive force (EMF) 6.0 V and internal resistance 0.50 Ω is connected to an external circuit. The external circuit consists of a 4.0 Ω resistor in series with a parallel combination of a 6.0 Ω resistor and a 3.0 Ω resistor.

Quantity	Value
EMF of cell, $\varepsilon$ε	6.0 V
Internal resistance, $r$r	0.50 Ω
Series resistor	4.0 Ω
Parallel pair	6.0 Ω and 3.0 Ω

(a) Show that the total resistance of the external circuit is 6.0 Ω. (2 marks)

(b) Calculate the current drawn from the cell and the terminal potential difference across its terminals. (3 marks)

(c) Calculate the total power dissipated in the external circuit. (1 mark)

A student investigates an electrical component X by recording the current through it for a range of potential differences. The readings are:

p.d. / V	0	1.0	2.0	3.0	4.0	5.0
Current / A	0	0.50	0.80	1.00	1.14	1.25

(a) Calculate the resistance of component X at a p.d. of 1.0 V and at a p.d. of 5.0 V. (2 marks)

(b) State, with reference to your results and the data, whether component X is an ohmic conductor. (2 marks)

(c) State, giving a reason, which single component from an ohmic resistor, a filament lamp and a semiconductor diode is most consistent with these data. (1 mark)

A greenhouse uses a temperature-sensing circuit to switch on a cooling fan when it becomes too hot. A potential divider is supplied by a 12 V source. A negative temperature coefficient (NTC) thermistor is connected between the positive terminal and the output point, and a fixed 3.0 kΩ resistor is connected between the output point and the 0 V terminal. The output voltage is taken across the fixed 3.0 kΩ resistor and fed to a control unit that switches the fan on when the output reaches 8.0 V or more.

The thermistor has a resistance of 9.0 kΩ on a cold morning and 1.0 kΩ on a hot afternoon.

(a) Calculate the output voltage on the cold morning and on the hot afternoon. (3 marks)

(b) Use your results to explain whether the fan switches on at the hotter temperature, and why this arrangement is suitable for the sensor's purpose. (2 marks)

An engineer is designing the heating element of an electric heater using nichrome wire, which has a resistivity of $\rho = 1.1 \times 10^{-6} \ \Omega \ \text{m}$ρ=1.1×10−6 Ω m. The element is to be made from a length of 1.5 m of nichrome wire of uniform diameter 0.30 mm.

(a) Calculate the resistance of this length of nichrome wire. (3 marks)

(b) The element is connected across the 230 V mains supply. Calculate the power dissipated by the element. (1 mark)

Kirchhoff's two circuit laws follow from the conservation of two physical quantities.

(a) State Kirchhoff's first law and Kirchhoff's second law, naming the conserved quantity that each law expresses. (2 marks)

(b) At a junction in a circuit, currents of 2.5 A and 1.5 A flow into the junction along two separate wires, and a single wire carries current out of the junction. State the current in the wire leaving the junction. (1 mark)