The potentiometer circuit shown in Fig. 5.1 is arranged for comparing potential differences. A cell with e.m.f. $E_1$ and internal resistance $r_1$ is placed in series with a resistor of resistance $R_1$ and a uniform metal wire whose total resistance is $R_2$. A second cell with e.m.f. $E_2$ and internal resistance $r_2$ is connected in series with a sensitive ammeter, and this combination is then connected across the wire at $B\,J$. The contact at $J$ lies halfway along the wire. The directions of the currents are indicated in Fig. 5.1.
(a(i))[1]
Use Kirchhoff’s laws to find the connection between the currents $I_1$, $I_2$ and $I_3$.
(a(ii))[1]
Use Kirchhoff’s laws to find the relationship between $E_1$, $R_1$, $R_2$, $r_1$, $I_1$ and $I_2$ in loop $H\,B\,J\,F\,G\,H$.
(a(iii))[2]
Use Kirchhoff’s laws to obtain the relationship between $E_1$, $E_2$, $r_1$, $r_2$, $R_1$, $R_2$, $I_1$ and $I_3$ in the loop $H\,B\,C\,D\,J\,F\,G\,H$.
(b)[2]
The contact at $J$ is shifted along the wire. Explain why the ammeter reading alters.