Question

A voltage of peak value $283V$ and varying frequency is applied to a series $LCR$ combination in which $R=3$ $\Omega$, $L=25mH$ and $C=400$ $\mu F$. The frequency (in $Hz$) of the source at which maximum power is dissipated in the above circuit is

• A. $100.2$
• B. $25.3$
• C. $75.4$
• D. $50.3$

Answer 1

The correct option is D $50.3$

Given,
$V=283VR=3\Omega L=25mHC=400\mu F$

In a series $LCR$ circuit, maximum power will be dissipated at resonant frequency, which is given as,
$f_r=\frac{{\omega }_r}{2\pi }=\frac{1}{2\pi \sqrt{LC}}=\frac{1}{2\pi \sqrt{(25\times {10}^{-3})\times (400\times {10}^{-6})}}=50.3Hz.$.