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A $60 W / 120 V$ bulb is connected to a $240 / 60 Hz$ supply with an inductance in series. Find the value of inductance so that bulb gets correct voltage -

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$\frac{2 \sqrt{3}}{π} H$

$2 \sqrt{3} H$

$\frac{2.3}{π} H$

$π H$

answer is D.

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Detailed Solution

$R = \frac{(120)^{2}}{60} = 240 Ω$ we require $i = 0.5 A$
$| Z | = 480 Ω$
$X_{L} = \sqrt{480^{2} - 240^{2}} = 240 \sqrt{3} Ω$
$L = \frac{240 \sqrt{3}}{60 \times 2 π} = \frac{2 \cdot \sqrt{3}}{π} H$

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