Question

In an AC RL series circuit, the potential difference across the resistor and inductor is $40\text{V}$ and $30\text{V}$ respectively. What will be the average power utilized by this circuit, if a current of $5\text{A}$ flows through it?

• A. $100\text{W}$
• B. $200\text{W}$
• C. $500\text{W}$
• D. $700\text{W}$

Answer 1

The correct option is B $200\text{W}$

$E_{\text{rms}}=\sqrt{V_R^2+V_L^2}=\sqrt{{40}^2+{30}^2}=50\text{V}$

Also,

$V_R=I_{\text{rms}}R\Rightarrow R=\frac{V_R}{I_{\text{rms}}}=\frac{40}{5}=8\Omega$

and,

$V_L=I_{\text{rms}}{X}_L\Rightarrow X_L=\frac{V_L}{I_{\text{rms}}}=\frac{30}{5}=6\Omega$

Further,

$Z=\sqrt{R^2+X_L^2}=\sqrt{8^2+6^2}=10\Omega$

Therefore, average power utilized,

$P_{\text{avg}}=E_{\text{rms}}{I}_{\text{rms}}\cos \varphi$

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

$\Rightarrow P_{\text{avg}}=50\times 5\times \frac{8}{10}=200\text{W}$

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