Question

Given below are two statements.

Assertion : Peak value of AC through a resistor of $10\Omega$ is $2\text{A}$. Then, average power consumed by the resistor should be $20\text{W}$.

Reason : Average power consumed by a resistor is, $P={i_{\text{rms}}}^{2}R$

Based on the above statements, choose the correct alternative.

• A. Both assertion and reason are true, and the reason is a correct explanation of the assertion.
• B. Both assertion and reason are true, but the reason is not a correct explanation of the assertion.
• C. Assertion is true, but the reason is false.
• D. Assertion is false, but the reason is true.

Answer 1

The correct option is A Both assertion and reason are true, and the reason is a correct explanation of the assertion.

The average power consumed by a resistor,

$P_{\text{avg}}=E_{\text{rms}}{i}_{\text{rms}}\cos \varphi =i_{\text{rms}}R\times i_{\text{rms}}\times \cos 0^{\circ }={i_{\text{rms}}}^{2}R$

Now,

$P_{\text{avg}}={i_{\text{rms}}}^{2}R={\left(\frac{i_0}{\sqrt{2}}\right)}^{2}R=\frac{2^2}{2}\times 10=20\text{W}$

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