For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5nF

Question

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is \(2.5 \mathrm{nF}\). If resistance of \(200 \Omega\) and \(100 \ \mathrm{mH}\) inductor is being used in the given circuit. The frequency of ac source is ______ \(\times 10^{3} \mathrm{~Hz}\) (given \(\pi^{2}=10\) )

Answer 1

Correct answer is : 10 

for maximum current \(\rightarrow X_C=X_L \)

\( \omega \mathrm{L}=\frac{1}{\omega \mathrm{c}} \Rightarrow \omega^2=\frac{1}{100 \times 10^{-3} \times 2.5 \times 10^{-9}}\) 

\(\omega^2=\frac{10^{12}}{250}=\frac{10^{11}}{25}=0.04 \times 10^{11}=4 \times 10^9\) 

\((2 \pi \mathrm{f})^2=4 \times 10^9 \)

 \(4 \pi^2 \mathrm{f}^2=4 \times 10^9 \) 

\( \mathrm{f}^2=10^8 \Rightarrow \mathrm{f}=10^4 \mathrm{H}_2\) 

\( \mathrm{f}=10 \times 10^3 \mathrm{H}_2 \)