Question

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

• A. $1mH$
• B. Cannot be calculated unless $R$ is known
• C. $10mH$
• D. $100mH$

Answer 1

Answer: (D)

In series LCR, the current is maximum at resonance.
$\therefore$ Resonant frequency, $\omega =\frac{1}{\sqrt{\text{LC}}}$
$\therefore$ ${\omega }^2=\frac{1}{\text{LC}}$ or, $\text{L}=\frac{1}{{\omega }^2\text{C}}$
Given, $\omega =1000{\text{ s}}^{-1}$ and $\text{C}=10\mu \text{F}$
$\therefore$ $\text{L}=\frac{1}{1000\times 1000\times 10\times 10^{-6}}=\text{0.1}\text{ H}=100\text{ mH}$