Upon a six fold increase in the external resistance of a circuit, the voltage across the terminals of the battery has increased from 5V to 10V. The e.m.f. of the battery
Answer & explanation
Correct answer: option 3
$ E \frac{R}{R+r} = 5V$ ...........(1)
$ E \frac{6R}{6R+r} = 10 V$ ...........(2)
Dividing equation (1) and (2)
$\frac{R}{6R} \frac{6R+r}{R+r} = \frac{5}{10}$
$\Rightarrow \frac{6R+r}{R+r} = 3 $
$ 6R+r = 3R + 3r$
$ r = 1.5R$
$\Rightarrow E = 5\frac{R+r}{R} = 12.5V$