Question

In the circuit shown, when dc of $250$V is applied, one ampere current passes through the circuit and when an alternating voltage source of $250$V and $2250$rad/s is applied, current of $1.25$A flows. If maximum current flows through the circuit at a frequency of $4500$ rad/s, then the value of L and C will be respectively.

• A. $0.295$H, ${10}^{-4}$F
• B. $0.0752$H, $0.01$F
• C. $0.0392$H, $0.005$F
• D. $0.0494$H, ${10}^{-6}$F

Answer 1

The correct option is D $0.0494$H, ${10}^{-6}$F

When DC is applied, the resistor is effective

$R=\frac{V}{i_1}=\frac{250}{1}=250\Omega$

The impedance of LC branch

$Z=X_L-X_C=({\omega }_L-\frac{1}{{\omega }_C})$

current in LC- branch

$i_z=\frac{V}{Z}=\frac{250}{({\omega }_L-\frac{1}{{\omega }_C})}$

The net current $i=\sqrt{i_1^2+i_2^2}$

$i_2=\sqrt{i^2-i_1^2}$

$=\sqrt{{1.25}^2-1^2}=0.75A$

in eq (1) we have,

$0.75=\frac{250}{|{\omega }_L-\frac{1}{{\omega }_C}|}$

$\Rightarrow {\omega }_0=\frac{1}{\sqrt{LC}}$

$4500=\frac{1}{\sqrt{LC}}$

(D) $L=\frac{4}{81}HC=1\mu F$