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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Verified Solution

Answer & Solution

Correct Answer

(B) \(0.8\, H\) and \(250\, \mu F\)

Detailed explanation

Current through \(60 \Omega\) resistance \(=\frac{15}{60}=\frac{1}{4} A\)

thus capacitor current \(=\frac{1}{4} A\)

\(\because V _{ C }= I X _{ C }\)

\(10=\frac{1}{4} \times \frac{1}{\omega C}\)

\(\therefore C =\frac{1}{40 \omega}=\frac{1}{4000}=250 \mu F\)

Now,

current through \(40 \Omega\) resistance \(=\frac{20}{40}=\frac{1}{2} A\)

thus current through inductor \(=\frac{1}{2}-\frac{1}{4}=\frac{1}{4} A\)

\(V _{ L }= IX _{ L }=\frac{1}{4} \times \omega L\)

\(20=\frac{1}{4} \times 100 \times L\)

\(\Rightarrow L =0.8 H\)

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