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
• E. 5

Answer 1

Answer: (D)

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

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

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