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An electric lamp which runs at $100 V$ DC and consumes $10 A$ current is connected to AC circuit at $150 V$ , $50 H z$ cycles with a choke coil in series. Calculate the inductance and drop of voltage across the choke. Neglect the resistance of choke.

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$0.036 H; 111.8 V$

$0.036 H; 110.8 V$

$0.36 H; 111.8 V$

$111.8 H; 0.036 V$

answer is A.

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Detailed Solution

$\begin{array}{rcl} V_{L} & = & \sqrt{V^{2} - V_{R}^{2}} \\ = & \sqrt{{(150)}^{2} - {(100)}^{2}} \\ = & 111.8 V \end{array}$

Since, $V_{L} = I X_{L} = I (2 πfL)$

Therefore, $L = \frac{V_{L}}{2 πfI} = \frac{111.8}{2 π \times 50 \times 10} = 0.036 H$

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