Question

When a voltage $V=V_{0} \cos \omega t$ is applied across a resistor of resistance $R$, the average power dissipated per cycle in the resistor is given by

• A. $\frac{V_{0}}{\sqrt{2} R}$
• B. $\frac{V_{0}}{\sqrt{2} \omega R}$
• C. $\frac{V_{0}^{2}}{2 R}$
• D. $\frac{V_{0}^{2}}{2 \omega R}$

Answer 1

Answer: (C)

$P=E_{ \text{rms }} I_{ \text{rms }} \cos \phi$
$\cos \phi=\frac{R}{Z}$
$\cos \phi=1$ for resistor
$V_{ \text{rms }}=\frac{V_{0}}{\sqrt{2}}$
$P=\frac{V_{0}}{\sqrt{2}}, \frac{V_{0}}{R \sqrt{2}}(1)$
$\left(\because I_{ \text{rms }}=\frac{V_{ \text{rms }}}{R}=\frac{V_{0}}{R \sqrt{2}}\right)$
$P=\frac{V_{0}^{2}}{2 R}$