State Kirchhoff’s first law in words.
A cell with internal resistance $r$ is joined to two resistors of resistances $R_1$ and $R_2$ as shown in Fig. 6.1. The p.d.s across $R_1$ and $R_2$ are $V_1$ and $V_2$ respectively. The terminal p.d. across the cell is $V$. The current in the circuit is $I$. Use Kirchhoff’s laws to show that the total resistance $R_T$ of the external circuit is given by $R_T = R_1 + R_2$.
The e.m.f. of the cell in Fig. 6.1 is $1.50\,\text{V}$. The values of $R_1$ and $R_2$ are $10\,\Omega$ and $15\,\Omega$ respectively. The terminal p.d. of the cell is $1.35\,\text{V}$. Calculate the internal resistance $r$ of the cell.
A resistor of resistance $R_3$ is added to the circuit in Fig. 6.1, so that the circuit is shown in Fig. 6.2. State and explain the effect, if any, of this change on (i) the current in the cell, (ii) the terminal p.d. of the cell.