Question

The value of inductance $L$ for which the current is maximum in series LCR circuit with $C=10\mu F$ and $\omega =1000rad{s}^{-1}$ .

• A. $10mH$
• B. $50mH$
• C. $200mH$
• D. $100mH$

Answer 1

Answer: (D)

In resonance condition, maximum current flows in the circuit.
Current in the LCR circuit is given by
$i=\frac{V}{\sqrt{R^2+{\left(X_L-X_C\right)}^2}}$
For current to be maximum denominator should be minimum.
${\left(X_L-X_C\right)}^2=0$
$\Rightarrow X_L=X_C$
$\Rightarrow \omega L=\frac{1}{\omega C}$
$\therefore L=\frac{1}{{\omega }^{2}C}$
$=\frac{1}{{\left(1000\right)}^2\times 10\times {\left(10\right)}^{-6}}$
$=\frac{1}{10}H$
$\therefore L=0.1H=100mH$