The angular frequency of alternating current in a L-C-R circuit is… | JEE Main 2021 (25 Feb, Shift 1)

Q50JEE Main 2021 · 25 FEB · SHIFT 1Medium

Series LCR Circuit

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

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Answer: (b)

Current through $R$ : $I = \frac{15}{60} = 0.25$ A; the same current flows through $C$ .
$X_C = \frac{10}{0.25} = 40\ \Omega \Rightarrow C = \frac{1}{\omega X_C} = \frac{1}{100 \times 40} = 250\ \mu$ F
The $R'$ branch is broken (gap shown), so the full 0.25 A goes through $L$ : $X_L = \frac{20}{0.25} = 80\ \Omega$
$L = \frac{X_L}{\omega} = \frac{80}{100} = 0.8$ H
So the answer is (b) 0.8 H and 250 $\mu$ F.

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