An electric lamp designed for operation on 110 V AC is connected to a 220V AC supply, through a choke coil of inductance 2H, for proper operation. The angular frequency of the AC is $100 \sqrt{10} rad / s$ . If a capacitor is to be used in the place of the choke coil, its capacitance must be:

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$1 μ F$

$2 μ F$

$5 μ F$

$10 μ F$

answer is C.

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Detailed Solution

The total impedence in LR and RC circuit should be equal.

I.e.,

$Z = \sqrt{R^{2} + X_{L}^{2}} = \sqrt{R^{2} + X_{C}^{2}} \Rightarrow X_{C} = X_{L} \Rightarrow \frac{1}{ωC} = ωL \Rightarrow C = \frac{1}{ω^{2} L} \Rightarrow C = \frac{1}{{(100 \sqrt{10})}^{2} \times 2} \Rightarrow C = 5 μF$

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