Question:
A cell of emf E and internal resistance r is connected across an external resistance R. Plot a graph showing the variation of PD across R versus R.
Solution:
We know that $I=\frac{E}{R+r}$ and V=IR.
So $V=\frac{E R}{R+r} \ldots($ (I)
$V=\frac{E}{1+\frac{\gamma}{R}} \ldots$ (II)
Here $\mathrm{E}, \mathrm{r}$ are constants. So
$V \propto \frac{1}{1+\frac{\gamma}{R}}($ from II $)$
and $I$ oc $R$ (from I)
With increase in $\mathrm{R}$, P.D. across $\mathrm{R}$ is increased upto maximum value E.