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

The correct option is A $1\Omega$

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 equation (i)
$0.8=\frac{4}{2(4-2r)+r}$
$0.8=\frac{4}{8-3r}$
$8-3r=5$
$r=1\Omega$