Question

When a current of $2\,A$ flows in a battery from negative to positive terminal, the potential difference across it is $12 \,V$. If a current of $3\,A$ flowing in the opposite direction produces a potential difference of $15\, V$, 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 $\varepsilon$ be emf and $r$ be internal resistance of the battery.
In first case,
$12 = \varepsilon - 2r \quad ...(i)$
In second case,
$15 = \varepsilon + 3r \quad...(ii)$
Subtract $(i)$ from $(ii)$, we get
$r = \frac{3}{5} \Omega$
Putting this value of $r$ in eqn. $(i)$, we get
$\varepsilon = 12 + \frac{2\times 3}{5} $
$ = \frac{60+6}{5}$
$= \frac{66}{5} = 13.2\,V$