MHT CET · Physics · Alternating Current
In series L-C-R circuit \(C=2 \mu \mathrm{F}, L=1 \mathrm{mH}\) and \(R=10 \Omega\). What is the ratio of energies stored in the inductor and the capacitor, when the maximum current flows in the circuit?
- A \(1: 8\)
- B \(5: 1\)
- C \(1: 5\)
- D \(8: 1\)
Answer & Solution
Correct Answer
(C) \(1: 5\)
Step-by-step Solution
Detailed explanation
At maximum current condition, system is at resonance condition.
\(\therefore X_C=X_L\)
\(\Rightarrow \frac{U_C}{U_L}=\frac{\frac{1}{2} C V^2}{\frac{1}{2} L i^2}=\frac{C i^2 R^2}{L i^2}\)
\(\Rightarrow \frac{U_C}{U_L}=\frac{2 \times 10^{-6}}{10^{-3}} \times 100\)
Hence, we get
\(\frac{U_C}{U_L}=\frac{2}{10}=\frac{1}{5}\)
\(\therefore X_C=X_L\)
\(\Rightarrow \frac{U_C}{U_L}=\frac{\frac{1}{2} C V^2}{\frac{1}{2} L i^2}=\frac{C i^2 R^2}{L i^2}\)
\(\Rightarrow \frac{U_C}{U_L}=\frac{2 \times 10^{-6}}{10^{-3}} \times 100\)
Hence, we get
\(\frac{U_C}{U_L}=\frac{2}{10}=\frac{1}{5}\)
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