Question

When a current of 2 A 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. 12.6 V
• B. 13.2 V
• C. 13.5 V
• D. 14.0 V

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
$\epsilon =12+\frac{2\times 3}{5}=\frac{60+6}{5}=\frac{66}{5}=13.2V$