Question

A circuit whose resistance $R$ is connected to $n$ similar cells. If the current in the circuit is the same whether the cells are connected in series or parallel, then the internal resistance $r$ of each cell is given by

• A. $r=\frac{R}{n}$
• B. $r=nR$
• C. $r=R$
• D. $r=\frac{1}{R}$

Answer 1

The correct option is C $r=R$

When the cells are connected in series, current $I_1$ is given by:

$I_1=\frac{n\epsilon }{R+nr}......\left(1\right)$

When the cells connected in parallel, current $I_2$ is given by:

$I_2=\frac{\epsilon }{R+\frac{r}{n}}=\frac{n\epsilon }{nR+r}.....\left(2\right)$

As, $I_1=I_2$

So, $\frac{n\epsilon }{R+nr}=\frac{n\epsilon }{nR+r}$

$\Rightarrow R+nr=nR+r$

$\Rightarrow (n-1)r=(n-1)R$

$\therefore r=R$

Hence, the correct answer is option $\left(c\right)$.