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  4. 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

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Q. 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

Current Electricity

Solution:

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