Question

A galvanometer connected with an unknown resistor and two identical cells in series each of emf $2 \,V$ shows a current of $1\, A$. If the cells are connected in parallel, it shows $0.8\, A$. 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
$i=\frac{n E}{R+n r}$
$1=\frac{2 \times 2}{R+2 r}$
$R+2 r=4\,...(i)$
Again, in parallel the current
$i =\frac{E}{R+\frac{r}{n}}$
$0.8 =\frac{2}{R+\frac{r}{2}} $
$0.8 =\frac{2 \times 2}{2 R+r}$
From Eq. (i)
$0.8 =\frac{4}{2(4-2 r)+r} $
$0.8 =\frac{4}{8-3 r} $
$8-3 r =5 $
$r =1 \Omega$