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In a series LCR circuit, L = 1 microH, C = 1 microF, and R = 1 kilo-ohm, connected to an AC source V = V₀ * sin(omega * t). Which of the following statements is/are correct?

1. The angular frequency at which current is in phase with the voltage is independent of R.
2. At omega approximately 0, the current in the circuit becomes nearly zero.
3. At omega >> 10⁶ rad/s, the circuit behaves like a capacitor.
4. The current will be in phase with the voltage at omega = 10⁴ rad/s.

Correct answer: The angular frequency at which current is in phase with the voltage is independent of R.

Solution

Resonance occurs when omega₀ = 1/sqrt(LC) = 1/sqrt(10⁻⁶ * 10⁻⁶) = 10⁶ rad/s, independent of R. At omega=0 the capacitor blocks DC so I=0. At very high omega, X_L = omega*L >> X_C, so the circuit is inductive (not capacitive). The resonant omega is 10⁶ rad/s, not 10⁴ rad/s.

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