Question

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

• A. $0.8H$ and $150\mu F$
• B. $0.8H$ and $250\mu F$
• C. $1.33H$ and $250\mu F$
• D. $1.33H$ 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 $=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}A$
$V_L=I{X}_L=\frac{1}{4}\times \omega L$
$20=\frac{1}{4}\times 100\times L$
$\Rightarrow L=0.8H$