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A series LCR circuit contains inductance \( 5 \mathrm{mH} \), capacitance \( 2 \mu \mathrm{F} \) and resistance \( 10 \Omega \). If a
frequency A.C. source is varied, what is the frequency at which maximum power is dissipated
\( ? \)
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frequency A.C. source is varied, what is the frequency at which maximum power is dissipated
\( ? \)
Solution:
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Verified Answer
The correct answer is:
\( \frac{5}{\Pi} \times 10^{3} H z \)
Maximum power is dissipated at resonance
\(L=5 m H\) and \(C=2 \mu F\
The resonant frequency
\(\begin{aligned} f_{R} &=\frac{1}{2 \pi \sqrt{L C}} \\ &=\frac{1}{2 \pi \sqrt{5 \times 10^{-3} \times 2 \times 10^{-6}}} \\ &=\frac{1}{2 \pi \sqrt{10^{-8}}}=\frac{1}{2 \pi \times 10^{-4}} \\ &=\therefore F_{R}=\frac{10 \times 10^{3}}{2 \pi}=\frac{5 \times 10^{3}}{\pi} H z \end{aligned}\)
\(L=5 m H\) and \(C=2 \mu F\
The resonant frequency
\(\begin{aligned} f_{R} &=\frac{1}{2 \pi \sqrt{L C}} \\ &=\frac{1}{2 \pi \sqrt{5 \times 10^{-3} \times 2 \times 10^{-6}}} \\ &=\frac{1}{2 \pi \sqrt{10^{-8}}}=\frac{1}{2 \pi \times 10^{-4}} \\ &=\therefore F_{R}=\frac{10 \times 10^{3}}{2 \pi}=\frac{5 \times 10^{3}}{\pi} H z \end{aligned}\)
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