Question

After the external resistance of a circuit has been increased 5 times, the voltage across the battery terminals increases from $10V$ to $30V$. The emf of the battery is

• A. 60V
• B. 30V
• C. 40V
• D. 50V

Answer 1

The correct option is A 60V

Case 1

$I=\frac{E}{R+r}$
P.D across battery $=IR$

$=\frac{ER}{R+r}=10$ ........(1)
Case 2

$I=\frac{E}{5R+r}$
P.D across battery $=I\left(5R\right)$

$=\frac{5ER}{5R+r}=30$ .......(2)
Dividing (1) by (2)

$\frac{5R+r}{5(R+r)}=\frac{1}{3}\Rightarrow 15R+3r=5R+5r$

$2r=10R$

$r=5R$
$\Rightarrow \frac{ER}{R+5R}=10\Rightarrow \frac{ER}{6R}=10\Rightarrow E=60V$