Question

A capacitor $C=2\mu \text{F}$ and an inductor with $L=10\text{H}$ and coil resistance $5\Omega$ are in series in a circuit. When an alternating current of $rms$ value $2\text{A}$ flows in the circuit, the average power $\left(\text{in W}\right)$ in the circuit is

• A. $100$
• B. $50$
• C. $20$
• D. $10$

Answer 1

The correct option is C $20$

Average power in the circuit is

$P=V_{rms}{i}_{rms}\cos \varphi$

As, $V_{rms}=i_{rms}Z$ and $\cos \varphi =\frac{R}{Z}$

$\Rightarrow P=i_{rms}^{2}Z\times \frac{R}{Z}=i_{rms}^{2}R$

$=2^2\times 5=20\text{W}$

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