Question

Heat is produced at a rate given by $H$ in a resistor when it is connected across a supply of voltage $V$. If now the resistance of the resistor is doubled and the supply voltage is made $V/3$, then the rate of production of heat in the resistor will be

• A. $\frac{H}{18}$
• B. $\frac{H}{9}$
• C. $6H$
• D. $18H$

Answer 1

The correct option is A $\frac{H}{18}$

We know: $H=\frac{V^2}{R}$
Here, in second condition $V^{\prime }$ becomes $\frac{V}{3}$ and $R^{\prime }$ becomes $2R$.
So,
$H^{\prime }=\frac{{\left(\frac{V}{3}\right)}^2}{2R}=\frac{V^2}{18R}$

$H^{\prime }=\frac{H}{18}$