Unlike DC, an AC supply never sits still — its voltage sweeps from zero to a peak and back, then reverses, tracing a sine wave every cycle. Push that wave through a resistor, a coil, and a capacitor in turn, and each one treats it completely differently. Watch how.
An AC voltage is written v = Vmax sinωt. Egypt's mains run at 50 Hz — fifty full cycles every second. An ordinary moving-coil meter can't track a current that reverses that fast, so a hot wire ammeter instead measures the heating effect, which never reverses since Q ∝ I².
Now send that same wave through a plain resistor and watch how voltage and current line up.
v = Vmaxsinωt and i = V/R = Imaxsinωt rise and fall together — they reach zero, peak, and reverse at exactly the same instants. Voltage and current are in phase.
An inductor of zero resistance behaves nothing like this — its current lags the voltage.
The coil's self-induced back-emf, -LΔI/Δt, opposes the supply. Since ΔI/Δt is the slope of the current curve, the voltage waveform turns out to be a quarter-cycle ahead of the current: the voltage leads the current by 90°.
A capacitor swings the other way entirely — its voltage lags the current.
Current i = CΔV/Δt depends on how fast the plate voltage is changing — fastest right when V crosses zero. The current wave therefore runs a quarter-cycle ahead of the voltage: the voltage lags the current by 90°.
Mix resistance with reactance in one series circuit, and the vectors have to be added properly — that's impedance.
In series, the same current runs through every part, but each part's voltage sits at a different phase. Adding VR, VL and VC algebraically overshoots the real supply voltage; adding them as vectors gives Z = √(R² + (Xᵟ − XC)²).
The coil and capacitor store and return energy — they consume no power. Only R turns electrical energy into heat.
Take away the resistor entirely, and a coil and capacitor left alone will slosh energy back and forth forever — an oscillating circuit.
A charged capacitor discharges through an inductor. As its charge falls, the coil's current rises, storing the energy as a magnetic field. When the charge hits zero, the coil's collapsing field drives the current onward, recharging the capacitor with reversed polarity — and the cycle repeats at f = 1/(2π√(LC)).
Feed that oscillating circuit a range of frequencies and one stands out sharply — the resonance point used to tune a radio.
Sweep the AC supply's frequency across an LCR circuit and the current is small when far from f₀ = 1/(2π√LC), and largest exactly at f₀, where the inductive and capacitive reactances cancel. A radio receiver tunes its variable capacitor until the station's frequency matches f₀ and only that station's signal passes through.