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Q.

A capacitor of capacitance $100 μF$ and a coil of resistance $50 Ω$ and inductance 0.5H are connected in series with a 110 V, 50 Hz AC source. Find the rms value of the current.

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a

0.12 A

b

0.82 A

c

0.53 A

d

0.22 A

answer is B.

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Detailed Solution

$\begin{array}{l} I_{rms} = \frac{V_{rms}}{Z} = \frac{V_{rms}}{\sqrt{R^{2} + {(ωL - \frac{1}{ωC})}^{2}}} \\ = \frac{110}{\sqrt{(50)^{2} + {(2 π \times 50 \times 0 .5 - \frac{1}{2 π \times 50 \times 100 \times 10^{- 6}})}^{2}}} \\ = 0 .82 A \end{array}$

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