(a)[2]
Show that the equivalent resistance $R$ of the network satisfies $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$.
(b(i))[1]
Calculate the battery current.
(b(ii))[2]
Calculate the battery's internal resistance $r$.
(c)[2]
Resistors X and Y in Fig. 6.2 are made from wires with the same material and cross-sectional area. The mean drift speed of the free electrons in X is $2.1 \times 10^{-4}\,\text{m s}^{-1}$. Calculate the mean drift speed of the free electrons in Y.
(d)[2]
Resistor Z in Fig. 6.2 is replaced by a new resistor with a smaller resistance. State and explain what, if anything, happens to the terminal potential difference of the battery.