What you are looking at
A series circuit of a
resistor R,
inductor L and
capacitor C
driven by an alternating voltage. The oscilloscope shows the source voltage (violet) and the resulting
current (green); the graph on the right is the
resonance curve — how big the current gets at
each drive frequency. The circuit brightens as the current grows.
Reactance and impedance
In AC, the inductor and capacitor don't just resist — they push back with a frequency-dependent
reactance. The inductor opposes fast changes (X_L = ωL, growing with frequency); the
capacitor opposes slow ones (X_C = 1/ωC, shrinking with frequency). They act in opposition, and together with
R set the total
impedance:
Z = √( R² + (X_L − X_C)² ), I = V / Z
Resonance
At one special frequency the inductive and capacitive reactances are
equal and cancel. The
circuit then behaves as if only R were present, impedance drops to its minimum, and the current spikes to a
maximum:
X_L = X_C → f₀ = 1 / (2π√(LC))
Below f₀ the capacitor dominates (current
leads the voltage); above f₀ the inductor dominates
(current
lags). Right at f₀ they're in phase. Watch the green current trace slide into step with the
violet voltage exactly at the peak.
The quality factor
How sharp that peak is depends on the
quality factor Q:
Q = (1/R) · √(L/C)
A small resistance gives a tall, narrow peak (high Q) — the circuit is very selective, responding to a
narrow band of frequencies. That selectivity is exactly what lets a radio pick one station out of the crowd;
turning the dial changes C (or L), shifting f₀ to the station you want.
Things to try
Sweep the drive frequency and watch the current rise to a peak at f₀, then fall. Press "Tune to resonance" to
jump straight there. Lower R to sharpen the peak (raise Q); change L or C and watch f₀ move. Notice the phase
between voltage and current flip from leading to lagging as you cross resonance.