For a series LCR circuit, a graph of current i vs angular frequency omega is given. The half-power frequencies are omega1 and omega2 (omega1 < omega2). Which of the following statements is INCORRECT?

At resonance, angular frequency omega_r = sqrt(omega1 * omega2).
When omega = omega2 then source voltage leads the circuit current by pi/4.
When omega = omega_r then power factor of circuit is 1.
When omega = omega1 then power factor of circuit is sqrt(3)/2.

Correct answer: When omega = omega1 then power factor of circuit is sqrt(3)/2.

Solution

At half-power frequencies omega1 and omega2, the impedance magnitude is R*sqrt(2), the reactance equals R, and the phase angle between voltage and current is +-pi/4. Therefore power factor = cos(pi/4) = 1/sqrt(2), not sqrt(3)/2. Statement D is incorrect.

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