A) \[50\,\mu F\]
B) \[25\,\mu F\]
C) \[100\,\mu F\]
D) \[75\,\mu F\]
Correct Answer: A
Solution :
Capacitive reactance of an AC circuit containing only capacitor with an AC source is, \[{{X}_{C}}=\frac{1}{\omega C}\] or \[{{X}_{C}}=\frac{1}{2\pi f\,C}\] or \[C=\frac{1}{2\pi \,f\,{{X}_{C}}}\] Here, \[f=\frac{400}{\pi }Hz,\] \[{{X}_{C}}=25\,\,\Omega \] \[\therefore \] \[C=\frac{1}{2\pi \times \frac{400}{\pi }\times 25}=\frac{1}{2\times 400\times 25}\] \[=5\times {{10}^{-5}}F\] \[=50\,\mu F\]
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