Question

A cell of emf $E$ and internal resistance $r$ is connected in series with an external resistance $nr$ . Then, the ratio of the terminal potential difference to emf is $\frac{n}{n + \alpha }$ . Write the value of $\alpha $ .

Answer 1

For the given circuit, $i=\frac{E}{\left(n + 1\right) r}$

Potential drop across battery, $V_{T}=i\left(n r\right)= \, \frac{E}{\left(n + 1\right) r}\times \, nr$
Hece, $\frac{V_{T}}{E}=\frac{n}{n + 1}$