Q128 / 150 · MHT CET 2025 (27 Apr Shift 2) · Physics

In an LC circuit, angular frequency at resonance is ' $\omega$ '. What will be the new angular frequency when inductor's inductance is made two times and capacitor's capacitance is made four times?

  • Correct answer
    A
    $\frac{\omega}{2 \sqrt{2}}$
  • B
    $\frac{\omega}{\sqrt{2}}$
  • C
    $2 \omega$
  • D
    $\frac{2 \omega}{\sqrt{2}}$

Solution

The resonant angular frequency of an LC circuit is given by $\omega = \frac{1}{\sqrt{LC}}$.

When the inductance is doubled and the capacitance is quadrupled, the new values become $L' = 2L$ and $C' = 4C$.

The new resonant frequency is $\omega' = \frac{1}{\sqrt{L'C'}} = \frac{1}{\sqrt{(2L)(4C)}} = \frac{1}{\sqrt{8LC}}$.

This simplifies to $\omega' = \frac{1}{2\sqrt{2}\sqrt{LC}} = \frac{\omega}{2\sqrt{2}}$.

The new angular frequency is therefore $\frac{\omega}{2\sqrt{2}}$, which corresponds to option A.

Hence, the correct answer is option: 'A'.

Relevant Questions