Question

A galvanometer connected with an unknown resistor and two identical cells in series each of emf $2V$ shows a current of $1A$. If the cells are connected in parallel, it shows $0.8A$. Then the internal resistance of the cell is

• A. 1 $\Omega$
• B. 0.5 $\Omega$
• C. 0.25 $\Omega$
• D. 0.33 $\Omega$
• E. 0.66 $\Omega$

Answer 1

Answer: (A)

In series, the current
$i=\frac{nE}{R+nr}$
$1=\frac{2\times 2}{R+2r}$
$R+2r=4...(i)$
Again, in parallel the current
$i=\frac{E}{R+\frac{r}{n}}$
$0.8=\frac{2}{R+\frac{r}{2}}$
$0.8=\frac{2\times 2}{2R+r}$
From Eq. (i)
$0.8=\frac{4}{2(4-2r)+r}$
$0.8=\frac{4}{8-3r}$
$8-3r=5$
$r=1\Omega$