Question

In the given circuit the potential difference across reststance is 80 V and power consumed by it is 160 W.If AC frequency is 50 Hz find the value of L :-

• A. 0.3 H
• B. $\frac{0.3}{\pi }H$
• C. 10 H
• D. $\frac{0.7}{\pi }H$

Answer 1

The correct option is B $\frac{0.3}{\pi }H$

Given,

$V_{rms}=100V$

Potential across resistor, $V_R=80V$

$R=\frac{V_R^2}{P}=\frac{{80}^2}{160}=40\Omega$

$I=\frac{V_R}{R}=\frac{80}{40}=2A$

$I=\frac{V_{rms}}{\sqrt{R^2+{\left(2\pi fL\right)}^2}}$

$L=\frac{1}{2\pi f}\sqrt{{\left(\frac{V_{rma}}{I}\right)}^2-R^2}$

$L=\frac{1}{2\pi \times 50}\sqrt{{\left(\frac{100}{2}\right)}^2-{40}^2}=\frac{0.3}{\pi }H$

Hence, inductance is $\frac{0.3}{\pi }H$