1.1. Three resistors of resistances R₁, R₂ and R₃ are connected as shown in Fig. 1.1.

The currents in the resistors are I₁, I₂ and I₃. The total current in the combination of resistors is I and the potential difference across the combination is V.

Show that the total resistance R of the combination is given by the equation

$\frac{1}{R}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}+\frac{1}{{R}_{3}}$

1.2. A battery of electromotive force (e.m.f.) 6.0 V and internal resistance r is connected to an external resistor of resistance 12 Ω and a thermistor X, as shown in Fig. 1.2.

Fig. 1.2

(i) By considering energy, explain why the potential difference across the terminals of the battery is less than the e.m.f.

[1]

(ii) A charge of 2.5 kC passes through the battery.

Calculate:

• the total energy transferred by the battery

energy = ............................................................ J

• the number of electrons that pass through the battery.

number = .......................................

[3]

(iii) The combined resistance of the external resistor and thermistor X connected in parallel is 4.8 Ω.

Calculate the resistance of X.

resistance = ........................................ Ω [1]

(iv) Use your answer in (b)(iii) to determine the ratio

$\frac{powerdissipatedinthermistorX}{powerdissipatedin12 \Omega resistor}$

ratio = .................................. [2]

(v) The temperature of thermistor X is now decreased.

State and explain the effect, if any, of this temperature change on the total power produced by the battery.

[3]