Question

A capacitor has a capacity $C$ and reactance $X$. If the capacitance and frequency both are doubled, the reactance will become

• A.
  $4X$
• B.
  $X/2$
• C.
  $\frac{X}{4}$
• D.
  $2X$

Answer 1

The correct option is C

$\frac{X}{4}$
The capacitive Resistance is given by the formula

$X=\frac{1}{\omega C}=\frac{1}{2\pi fC}$

Where $C\to \text{Capacitance}f\to \text{Frequency}$

Now Since frequency is doubled & capacitance also Doubled

$\Rightarrow X^{\prime }=\frac{1}{2\pi \left(2f\right)\left(2C\right)}$

$=\frac{1}{4}\left(\frac{1}{2\pi fC}\right)=\left(\frac{X}{4}\right)$

Hence, $\left(C\right)$ is the correct answer.