Question

$N$ identical cells, whether joined together in series or in parallel, give the same current, when connected to an external resistance of $R$. The internal resistance of each cell is

• A. $r=NR$
• B. $r=R$
• C. $r=\frac{R}{N}$
• D. $r=N^{2}R$

Answer 1

The correct option is B $r=R$

Let $E$ be the emf of each cell and $r$ be the internal resistance of each cell.
In series, net emf $=NE$ and net internal resistance $=Nr$
Thus, current: $i_S=\frac{NE}{Nr+R}$
In parallel, net emf $=E$ and net internal resistance $=\frac{r}{N}$
Thus, current: $i_P=\frac{E}{r/N+R}$
Here, $i_S=i_P$
or, $\frac{NE}{Nr+R}=\frac{E}{r/N+R}$
or, $Nr+R=r+NR$
or, $R(1-N)=r(1-N)$
or, $r=R$