Question

A circuit consists of a resistance R connected to n similar cells. If the current in the circuit is the same whether the cells are connected in series or in 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 $r=R$

For n cells connected in series

$E_{eq}=nE$ And, $r_{eq}=nr$

So, $Current\left(I\right)=\frac{nE}{nr+R}$

Now,

For n cells connected in parallel

$E_{eq}=n$ And, $r_{eq}=\frac{r}{n}$

So, $Current\left(I^{\prime }\right)=\frac{nE}{(\frac{r}{n}+R)}$

But $I=I^{\prime }$

$\Rightarrow$ $\frac{nE}{nr+R}$ $=\frac{E}{n(\frac{r}{n}+R)}$

$\Rightarrow$ $\frac{nE}{nr+R}$ $=\frac{nE}{nR+r}$

$\Rightarrow r=R$

Therefore, C is correct option.