Question

The value of inductance $L$ for which the current is maximum in a series LCR A.C. circuit with $\text{C} = 1 0 \, \mu \text{F}$ and $\omega = 1 0 0 0 \text{ s}^{- 1}$ 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.
$∴ \, \, $ Resonant frequency, $\omega =\frac{1}{\sqrt{\textit{LC}}}$
$∴ \, \, $ $\omega ^{2}=\frac{1}{\textit{LC}}$ or, $\textit{L}=\frac{1}{\omega ^{2} \textit{C}}$
Given, $\omega = 1 0 0 0 \text{ s}^{- 1}$ and $\text{C} = 1 0 \, \mu \text{F}$
$∴ \, \, $ $\textit{L}=\frac{1}{1 0 0 0 \times 1 0 0 0 \times 1 0 \times 1 0^{- 6}}=\text{0.1}\text{ H}=100\text{ mH}$