Question

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

• A. $52.5$
• B. $50.3$
• C. $53.1$
• D. $56.7$

Answer 1

The correct option is B $50.3$

Given:

$V_0=283\text{V},R=3\Omega ,L=25\times {10}^{-3}\text{H}$

$C=400\mu \text{F}=4\times {10}^{-4}\text{F}$

Maximum power is dissipated at resonance, at which

$\omega =\frac{1}{\sqrt{LC}}$

$\Rightarrow 2\pi f=\frac{1}{\sqrt{LC}}$

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

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

Hence, option $\left(D\right)$ is correct.