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  4. Reactance of a capacitor of capacitance C μ F for A C frequency (400/π) Hz is 25 Ω, the value of C is:

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Q. Reactance of a capacitor of capacitance $C\, \mu F$ for $A C$ frequency $\frac{400}{\pi} Hz$ is $25\, \Omega$, the value of $C$ is:

Jharkhand CECEJharkhand CECE 2004

Solution:

Capacitive reactance $X_{C}$ is given by
$X_{C}=\frac{1}{\omega C}=\frac{1}{2 \pi f C}$
where, $\omega=2 \pi f$
Given, $X_{C}=25\, \Omega, f=\frac{400}{\pi} H z$
Hence, $25=\frac{1}{2 \pi \times \frac{400}{\pi} \times C}$
$ \Rightarrow C=\frac{1}{25 \times 800}=50 \,\mu F$