QJEEM24Ph8055: JEE Main 2024 Physics - Class 12 JEEM24Ph8055 Solution: In series LCR circuit, the capacitance is changed from to . To…

The resonance frequency $f_0$ of an LCR circuit is given by:

where:

• $L$ is the inductance.
• $C$ is the capacitance.

To keep the resonance frequency unchanged when the capacitance is changed from $C$ to $4C$ , we must adjust the inductance $L$ to a new value $L'$ such that:

Now solving for $L'$ :

Squaring both sides, we have:

Dividing both sides by $4C$ , we get:

Thus, the new inductance $L'$ is one fourth of the original inductance $L$ . Therefore, to achieve the same resonance frequency with the capacitance increased to $4C$ , the inductance should be reduced to a quarter of its initial value:

This means we have reduced the inductance by $\frac{3}{4}L$ , so the correct answer is:

Option C: reduced by $\frac{3}{4}L$