NEET Physics Electrostatics & Capacitance Question Bank NEET PYQ - Electrostatics and Capacitance

The reactance of a capacitor of capacitance C is X. If both the frequency and capacitance be doubled, then new reactance will be: [AIPMT 2001]

A) X

B) 2X

C) 4X

D) \[\frac{X}{4}\]

Correct Answer: D

Solution :

[d] If a capacitor of capacitance C is connected with an AC signal, then reactance of that circuit is purely capacitive.

The capacitive reactance is

\[X=\frac{1}{\omega C}=\frac{1}{2\,\pi \,f\,C}\] \[(\omega =2\,\pi \,f)\]

or \[X\,\,\propto \,\,\frac{1}{f\,C}\]

\[\therefore \] \[\frac{X'}{X}=\frac{fC}{f'C'}=\frac{f\times C}{2f\times 2C}\]

or \[\frac{X'}{X}=\frac{1}{4}\]

or \[X'=\frac{X}{4}\]