Question

In an oscillating $L-C$ circuit in which $C=4\mu \text{F}$, the maximum potential difference across the capacitor during the oscillations is $1.5\text{V}$ and the maximum current through the inductor is $50\text{mA}$. What is the frequency of the oscillations?

• A. $1.33\text{kHz}$
• B. $0.33\text{kHz}$
• C. $3.33\text{kHz}$
• D. $2.25\text{kHz}$

Answer 1

The correct option is A $1.33\text{kHz}$

Given, $C=4\mu \text{F};V_{max}=1.5\text{V};i_{max}=50\text{mA}$

Applying energy conservation principle,

$\frac{1}{2}C(V_{max}{)}^2=\frac{1}{2}L(i_{max}{)}^2$

$\Rightarrow 4\times {10}^{-6}\times (1.5{)}^2=L\times (50\times {10}^{-3}{)}^2$

$\Rightarrow L=3.6\times {10}^{-3}\text{H}$

$\therefore$ The oscillation frequency of $L-C$ circuit is

$f=\frac{1}{2\pi \sqrt{LC}}$

$=\frac{1}{2\pi \sqrt{(3.6\times {10}^{-3})\times (4\times {10}^{-6})}}$

$=\frac{1}{2\pi \times 6\times 2\times {10}^{-5}}$

$=1.33\times {10}^3\text{Hz}=1.33\text{kHz}$