Lcr Circuit

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In a series LCR circuit, R=10Ω, XL=20Ω, and XC=20Ω. The impedance of the circuit is:

RankGuru · Accepted Answer

1. **Impedance Formula**: In a series LCR circuit, $Z = \sqrt{R^2 + (X_L - X_C)^2}$.
2. **Condition of Resonance**: Here, $X_L = 20	ext{ \Omega}$ and $X_C = 20	ext{ \Omega}$. Since $X_L = X_C$, the circuit is in resonance.
3. **Calculation**: $Z = \sqrt{10^2 + (20 - 20)^2} = \sqrt{100} = 10	ext{ \Omega}$.
4. **Conclusion**: At resonance, the impedance is equal to the resistance.

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Lcr Circuit

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