Resonance condition for a series RLC circuit.

• A. ω0 = 1/√(LC)
• B. ω0 = √(LC)
• C. ω0 = L/C
• D. ω0 = 1/(LC)

Answer: (A)

At resonance in a series RLC circuit, the reactive effects of the inductor and capacitor cancel each other. This happens when the inductive reactance equals the capacitive reactance in magnitude: ωL = 1/(ωC). Solve for ω to get ω0^2 = 1/(LC), so ω0 = 1/√(LC).

This frequency depends only on the values of L and C (the resistance doesn’t affect the resonance frequency in the ideal model). At this point the impedance is just R, the current is at its maximum for the given voltage, and energy sloshes between the magnetic field of the inductor and the electric field of the capacitor with the voltages across L and C canceling.

The other expressions don’t fit because they don’t have the correct units for angular frequency (1/s). √(LC) would have units of time, and 1/(LC) would have units of 1/s^2, not 1/s.