Question

A voltage of peak value $283V$ and varying frequency is applied to series $LCR$ combination in which $R=3\Omega$, $L=25mH$ 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, $V_0=283V$,
$R=3\Omega$,
$L=25\times 10^{-3}H$
$C=400\mu F=4\times 10^{-4}F$
Maximum power is dissipated at resonance, for which
$\upsilon =\frac{1}{2\pi \sqrt{LC}}$
$=\frac{1\times 7}{2\times 22\sqrt{25\times 10^{-3}\times 4\times 10^{-4}}}$
$=\frac{7\times 10^3}{44\sqrt{10}}$
$=50.3Hz$