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

The correct option is D 50.3

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

$\nu =\frac{1}{2\pi \sqrt{LC}}=\frac{1\times 7}{2\times 22\sqrt{25\times {10}^{-3}\times 4\times {10}^{-4}}}$

$=\frac{7\times {10}^3}{44\sqrt{10}}=50.3Hz$