Reconstruct a capacitor from the response curve

A fixed 4.0 V peak sinusoidal source drives a series RLC circuit. The peak of the current-amplitude curve is 0.25 A. The two half-power angular frequencies are 300 and 500 rad/s.

What capacitance follows from the constant-element series model?

Organize the givens & assumptions

Source amplitude: 4.0 V peak
Maximum current amplitude: 0.25 A
Half-power angular frequencies: 300 and 500 rad/s

Steady sinusoidal response; total series R, L and C are positive and frequency independent; source amplitude is constant. Half-power refers to resistor heating, not half current amplitude.

A $50\ \mu\mathrm F$
B $\frac{250}{3}\ \mu\mathrm F$
C $125\ \mu\mathrm F$
D $250\ \mu\mathrm F$

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