AC Circuits & Resonance

AC Resonance

In an AC circuit, the inductor and capacitor fight each other — one resists changes in current, the other resists changes in voltage, and their effects push in opposite directions. At one special frequency their opposing effects cancel out exactly, leaving minimal resistance to the current, so the current surges to its biggest value. This is resonance, and it is how a radio tunes into one station while ignoring the rest.

ω₀ = 1 / √(L · C)

• ω₀ — resonant angular frequency (rad/s): the frequency where the inductor and capacitor cancel and current peaks
• L — inductance (H): how strongly the inductor resists changes in current
• C — capacitance (F): how much charge the capacitor stores per volt across it

A radio tuning circuit has an inductor of 1 henry and a capacitor of 0.25 farads. What is the resonant frequency?

• L = 1 H
• C = 0.25 F

1. ω₀ = 1 / √(L · C)
2. ω₀ = 1 / √(1 H · 0.25 F)
3. ω₀ = 1 / √0.25 = 1 / 0.5

ω₀ = 2 rad/s

Same inductor, L = 1 H, but now C = 4 F. What is the new resonant frequency?

• ω₀ = 0.5 rad/s
• ω₀ = 2 rad/s
• ω₀ = 8 rad/s

If you increase the inductor's inductance L while keeping C the same, the resonant frequency ω₀…

• increases
• decreases
• stays exactly the same