Question

Five cells each of emf $E$ and internal resistance $r$ send the same amount of current through an external resistance $R$ whether the cells are connected in parallel or in series. Then the ratio $\left( \frac{R}{r} \right)$ is

• A. 2
• B. $\frac{1}{2}$
• C. $\frac{1}{5}$
• D. 1

Answer 1

Answer: (D)

1

Answer 2

The correct option is(D): 1

When $5$ cell are joined in parallel as shown,
$i=\frac{\text { net emf }}{\text { total resistance }}$

$i=\frac{5 \,E}{5 \,R+r}$
When $5$ cell are joined in series as shown,

$i=\frac{5\, E}{5\, r+R}$
So, according to the questions
$\frac{5 \,E}{5\, R+r}=\frac{5 \,E}{5\, r+R}$
$5\, R+r=5 \,r+R$
$4 \,R=4 \,r \Rightarrow \frac{R}{r}=\frac{4}{4}$
$\frac{R}{r}=1$