Question

When a current of $2A$ flows in a battery from negative to positive terminal, the potential difference across it is $12V$. If a current of $3A$ flowing in the opposite direction produces a potential difference of $15V$, the emf of the battery is

• A. $12.6V$
• B. $13.2V$
• C. $13.5V$
• D. $14.0V$

Answer 1

Answer: (B)

Let $\epsilon$ be emf and $r$ be internal resistance of the battery.
In first case,
$12=\epsilon -2r...(i)$
In second case,
$15=\epsilon +3r...(ii)$
Subtract $(i)$ from $(ii)$, we get
$r=\frac{3}{5}\Omega$
Putting this value of $r$ in eqn. $(i)$, we get
$\epsilon =12+\frac{2\times 3}{5}$
$=\frac{60+6}{5}$
$=\frac{66}{5}=13.2V$