As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is aπA. The value of a is __________

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As shown in the figure an inductor of inductance $200 mH$ is connected to an AC source of emf $220 V$ and frequency $50 Hz$ . The instantaneous voltage of the source is $0 V$ when the peak value of current is $\frac{\sqrt{a}}{π} A$ . The value of a is ___________.

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answer is 242.

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Detailed Solution

$\begin{aligned} f = 50 Hz \\ X_{L} = 2 π fL \\ = 2 π (50) (200 \times 10^{- 3}) \\ = 20 π Ω \\ i_{0} = \frac{V_{0}}{X_{L}} \Rightarrow \frac{V_{rms} \sqrt{2}}{X_{L}} \\ = \frac{(220) \sqrt{2}}{20 π} = \frac{11 \sqrt{2}}{π} \\ i_{0} = \frac{\sqrt{242}}{π} \end{aligned}$