In a scries \(LR\) circuit, power of \(400\, W\) is dissipated from a source of \(250\, V , 50\, Hz\). The power factor of the circuit is \(0.8 .\) In order to bring the power factor to unity, a capacitor of value \(C\) is added in series to the \(L\) and \(R\). Taking the value of \(C\) as \(\left(\frac{ n }{3 \pi}\right) \mu F ,\) then value of \(n\) is\(......\)

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Answer & Solution

Correct Answer

(D) \(400\)

Step-by-step Solution

Detailed explanation

\(P =\frac{ E _{ rms }^{2}}{ Z } \cos \phi\)

\(400=\frac{(250)^{2} \times 0.8}{ Z }\)

\(Z =25 \times 5=125\)

\(X _{ L }=125 \sin \phi=125 \times 0.6=75\)

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