Question

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

• A. $51.5$
• B. $50.7$
• C. $51.1$
• D. $50.3$

Answer 1

Answer: (D)

Here, $V_0 = 283\, V$,
$R = 3\Omega$,
$L = 25 \times 10^{-3}\, H$
$C = 400\,\mu F = 4 \times 10^{-4}\,F$
Maximum power is dissipated at resonance, for which
$\upsilon=\frac{1}{2\pi\sqrt{LC}}$
$=\frac{1\times7}{2\times22\sqrt{25\times10^{-3}\times4\times10^{-4}}}$
$=\frac{7\times10^{3}}{44\sqrt{10}}$
$=50.3\,Hz$