Question

A direct current of $4\text{A}$ and an alternating current of peak value $4\text{A}$ flow through resistance of $3\Omega \text{and}2\Omega$ respectively. The ratio of heat produced in the two resistances in same interval of time will be

Answer 1

Heat produced is given by $H=i^{2}Rt$
For DC supply,
$H_1=i_1^2{R}_{1}t=4^2\times 3t=48t$
And, For AC supply,
$H_2=i_{\text{rms}}^2{R}_{2}t={\left(\frac{i_2}{\sqrt{2}}\right)}^2{R}_{2}t={\left(\frac{4}{\sqrt{2}}\right)}^2\times 2t=16t$
So, the ratio would be
$\frac{H_1}{H_2}=\frac{48t}{16t}=3:1$

Hence, option $\left(B\right)$ is correct.