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A series RLC circuit is driven by a 1000 Hz generator. The inductance is 90.0 mH, the capacitance is 0.500 microfarad, and the magnitude of the phase angle is 60.0 deg (take pi² = 10). Which one of the following statements is INCORRECT?

1. Here current leads the voltage in phase
2. Here voltage leads the current in phase
3. Resistance of circuit is 80*pi/sqrt(3) ohm
4. At resonance omega = (sqrt(2)/3) * 10⁴ rad/s

Correct answer: Here current leads the voltage in phase

Solution

With omega = 2*pi*1000, X_L ~ 565 ohm and X_C ~ 318 ohm, so X_L > X_C: the circuit is inductive and voltage leads current. Therefore the statement 'current leads the voltage' is incorrect. R = (X_L - X_C)/tan60 = 80*pi/sqrt(3) ohm and omega_resonance = 1/sqrt(LC) = (sqrt(2)/3)*10⁴ rad/s are both correct.

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