Question

Two identical cells whether connected in parallel or in series gives the same current when connected to an external resistance $1.5\, \Omega$. Find the value of internal resistance of each cell.

• A. $1\, \Omega$
• B. $0.5\, \Omega$
• C. zero
• D. $1.5\, \Omega$

Answer 1

Answer: (D)

Let $n$ cells be in series and $m$ in parallel, then
$\frac{n E}{R+n r}=\frac{E}{R+\frac{r}{m}}$
$\Rightarrow n\left[R+\frac{r}{m}\right]=R+ n r$
$\Rightarrow n R m +n r=R m+ m n r$
$\Rightarrow 6+2 r=3+4 r$
$\Rightarrow 2 r=3 \Rightarrow R=1.5\, \Omega$