Question

The potential difference applied across a given resistor is altered so that the heat produced per second increase by a factor of 9. By what factor does the potential difference changes.

Answer 1

Heat generated, $H=I^{2}Rt=\frac{v^{2}t}{R}$
$\frac{H}{H^{\prime }}=\frac{V^2}{V^{\prime 2}}=\frac{1}{9}{V}^{\prime 2}=9V^2{V}^{\prime }=3V$
So the potential will incrase by a factor 3.