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GUJCET · Physics · Alternating Current
For LCR AC series circuit \(\mathbf{L}=25 \mathbf{~ m H , R}=3 \Omega\), \(C=62.5 \mu \mathrm{~F}\). What is the frequency of the source at which resonance occurs ?
- A 35.40 Hz
- B 100 Hz
- C 127.39 Hz
- D 21 Hz
Answer & Solution
Correct Answer
(C) 127.39 Hz
Step-by-step Solution
Detailed explanation
(C) 127.39 Hz
Resonance frequency
\(
\begin{aligned}
v_{0} & =\frac{1}{2 \pi \sqrt{\mathrm{LC}}} \\
\therefore v_{0} & =\frac{1}{2 \times 3.14 \times \sqrt{25 \times 10^{-3} \times 62.5 \times 10^{-6}}} \\
\therefore v_{0} & =\frac{1}{2 \times 3.14 \times 12.5 \times 10^{-4}} \\
\therefore v_{0} & =127.39 \mathrm{~Hz}
\end{aligned}
\)
Resonance frequency
\(
\begin{aligned}
v_{0} & =\frac{1}{2 \pi \sqrt{\mathrm{LC}}} \\
\therefore v_{0} & =\frac{1}{2 \times 3.14 \times \sqrt{25 \times 10^{-3} \times 62.5 \times 10^{-6}}} \\
\therefore v_{0} & =\frac{1}{2 \times 3.14 \times 12.5 \times 10^{-4}} \\
\therefore v_{0} & =127.39 \mathrm{~Hz}
\end{aligned}
\)
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