resonance rlc

Question

Resonant angular frequency ω0 in series RLC circuit?

RankGuru · Accepted Answer

1. **Impedance Formula**: $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_L = \omega L$ and $X_C = 1 / \omega C$.
2. **Condition for Resonance**: Resonance occurs when the current amplitude is maximum, which happens when impedance $Z$ is minimum.
3. **Minimizing Z**: This requires $X_L = X_C$, so the reactive components cancel each other out.
4. **Solving for Frequency**:
   - $\omega_0 L = \frac{1}{\omega_0 C} \implies \omega_0^2 = \frac{1}{LC}$
   - $\omega_0 = \frac{1}{\sqrt{LC}}$
5. **At Resonance**: The circuit behaves as a purely resistive circuit, and current is in phase with voltage.

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resonance rlc

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