Question

A coil has a resistance of $10\Omega$ and an inductance of $0.4\text{H}$. It is connected across an AC source of $6.5\text{V},\frac{30}{\pi }\text{Hz}$. The average power consumed in the circuit is

• A. $0.625\text{W}$
• B. $0.325\text{W}$
• C. $0.925\text{W}$
• D. $0.125\text{W}$

Answer 1

The correct option is A $0.625\text{W}$

Given:

$R=10\Omega$

$L=0.4\text{H}$

$E_{\text{rms}}=6.5\text{V}$

$f=\frac{30}{\pi }\text{Hz}$

So,

$Z=\sqrt{R^2+X_L^2}=\sqrt{R^2+(2\pi fL{)}^2}$

$\Rightarrow Z=\sqrt{{10}^2+{(2\pi \times \frac{30}{\pi }\times 0.4)}^2}=26\Omega$

$\therefore I_{\text{rms}}=\frac{E_{\text{rms}}}{Z}=\frac{6.5}{26}=0.25\text{A}$

Now, average power,

$P_{\text{avg}}=E_{\text{rms}}{I}_{\text{rms}}\frac{R}{Z}$

$\Rightarrow P_{\text{avg}}=6.5\times 0.25\times \frac{10}{26}=0.625\text{W}$

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