Question

A direct current of $5\text{A}$ and an alternating current of peak value $5\text{A}$ flows through resistances $1\Omega$ and $2\Omega$ respectively. Find the ratio of heat produced in the two resistances in the same interval.

• A. $1$
• B. $2$
• C. $3$
• D. $0.5$

Answer 1

The correct option is A $1$

In time $t$, heat produced by $DC$ current $I_1$is given as

$H_1=I_1^2{R}_{1}t$

$\Rightarrow H_1=\left(5{)}^2\right(1)t=25t$

The $rms$ value of $AC$ current is given as

$I_{rms}=\frac{i_0}{\sqrt{2}}=\frac{5}{\sqrt{2}}\text{A}$

Heat produced by the $rms$ current in time $t$ is given as

$H_2=i_{rms}^2{R}_{2}t$

$\Rightarrow H_2={\left(\frac{5}{\sqrt{2}}\right)}^2\left(2\right)t=25t$

$\therefore \frac{H_1}{H_2}=\frac{25t}{25t}=1$

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