Question

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.

• A. $0.8 H$ and $150 \mu F$
• B. $0.8 H$ and $250 \mu F$
• C. $1.33 H$ and $250 \mu F$
• D. $1.33 H$ and $150 \mu F$

Answer 1

Answer: (B)

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 $=\frac{1}{2}-\frac{1}{4}=\frac{1}{4} A$
$V _{ L }= IX _{ L }=\frac{1}{4} \times \omega L$
$20=\frac{1}{4} \times 100 \times L$
$\Rightarrow L =0.8 H$