Alternating Current: Resistance, Reactance, RMS Values and Resonance
Why the current in every wall socket flips direction fifty times a second — and how resistors, capacitors and coils each respond to it.
Big Idea: An alternating current (AC) changes direction and magnitude smoothly in time, following a sine curve. A resistor limits it by ordinary (active) resistance R; a capacitor and a coil limit it by reactance that depends on frequency. When the inductive and capacitive reactances become equal, the circuit hits resonance and lets the largest possible current through. These three ideas explain power grids, transformers and every radio dial.
By the end you will be able to:
- write the instantaneous laws i = Im sin ωt and u = Um sin ωt;
- convert between amplitude and RMS (effective) values with the factor √2;
- compute capacitive reactance XC = 1/(ωC) and inductive reactance XL = ωL;
- find the impedance Z of a series RLC circuit and apply Ohm's law for AC;
- state the resonance condition XL = XC and the resonant frequency f0 = 1/(2π√(LC)).