Question

Reactance of a capacitor of capacitance $C\mu F$ for AC frequency $\frac{400}{\pi }$ 0 Hz is $25\Omega .$ The value of C is:

• A. $50\mu F$
• B. $25\mu F$
• C. $100\mu F$
• D. $75\mu F$

Answer 1

Answer: (A)

Capacitive reactance of an AC circuit containing only capacitor with an AC source is
$X_C=\frac{1}{\omega C}$
or $X_C=\frac{1}{2\pi fC}$
or $C=\frac{1}{2\pi f{X}_C}$
Here, $f=\frac{400}{\pi }Hz,X_C=25\Omega$
$\therefore C=\frac{1}{2\pi \times \frac{400}{\pi }\times 25}=\frac{1}{2\times 400\times 25}$
$=5\times 10^{-5}F$
$=50\mu F$