State Kirchhoff’s second law.
State the conservation law from which Kirchhoff’s second law is derived.
A circuit includes a cell with internal resistance $r$ and two resistors with resistances $R_1$ and $R_2$, as shown in Fig. 5.1. The voltmeter reads the potential difference (p.d.) across the two resistors as $V$. The current in the cell is $I$.
Use Kirchhoff’s laws to prove that the total resistance $R_T$ of the external circuit satisfies $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$.
The electromotive force (e.m.f.) of the cell is $1.50\,\text{V}$. When $R_1$ and $R_2$ have values of $10\,\Omega$ and $15\,\Omega$ respectively, the voltmeter shows a p.d. of $1.38\,\text{V}$. Calculate the internal resistance $r$ of the cell.
A third resistor is connected in parallel with $R_1$ and $R_2$ in the circuit in Fig. 5.1. State and explain the effect, if any, of this change on the current in the cell.
A third resistor is connected in parallel with $R_1$ and $R_2$ in the circuit in Fig. 5.1. State and explain the effect, if any, of this change on the p.d. measured by the voltmeter.