Question

In the circuit shown in figure, the supply has a constant $rms$ value $V$ but variable frequency $f$. The frequency at which the voltage drop across $R$ is maximum is

• A. $100Hz$
• B. $500Hz$
• C. $300Hz$
• D. None of these

Answer 1

The correct option is B $500Hz$

Solution

REF.Image

The frequency across R will be maximum

(equal to the supplied voltage) at

resosnance - condition.

$V_R=R\frac{V}{\sqrt{R^2+(\omega L-\frac{1}{\omega C}{)}^2}}$

$V_R$ be max when $\omega L-\frac{1}{\omega C}=0$

$\Rightarrow {\omega }^2=\frac{1}{LC}\Rightarrow \omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{\frac{1}{\pi }\times {10}^{-6}\times \frac{1}{\pi }}}$

$\Rightarrow \omega =\pi \times {10}^3$ rad $LS\Rightarrow f=\frac{\omega }{2\pi }=500Hz$

Option - B is correct.