Impedance and Phasors in AC Circuits
Resistors, capacitors and inductors each set a different phase between current and voltage, and rotating phasors add those voltages without trigonometric identities. Impedance packages size and phase in one quantity.
What a learner can do afterwards
- States the reactance of a capacitor and an inductor and how each shifts the phase
- Adds voltages with a phasor diagram to get the impedance of a series RLC circuit
- Reads the phase angle between supply voltage and current off the diagram
1 · Read
Each lone AC element has its own personality. A resistor lets current track voltage exactly in step. A capacitor passes current first, with voltage lagging a quarter cycle behind and size scaled by Xc equals 1 over omega C. An inductor flips it: voltage leads, current lags a quarter cycle, scaled by XL equals omega L. Frequency treats them oppositely: capacitors open up at high frequency while inductors choke.
In a series RLC circuit the three voltage arrows refuse to line up, so draw them as phasors. Put resistor voltage along the current, capacitor voltage a quarter turn behind, inductor voltage a quarter turn ahead. The vector sum is the supply voltage. Its length gives Z equals sqrt(R squared plus (XL minus Xc) squared), and its angle gives the phase lag phi, with tan phi equal to (XL minus Xc) over R.
Read the diagram like a weather map. Below resonance the capacitor rules and current leads; above it the inductor rules and current lags. When XL matches Xc the two arrows wipe each other out and the circuit looks purely resistive. That cancellation is resonance: impedance bottoms at R and current peaks in step with the supply.
Work every series AC problem in this order. Compute XL and Xc first at the given frequency. Sketch the three arrows and read Z from the total length. Read phi from the tilt, then use the AC Ohm rule, current amplitude equals voltage amplitude over Z. Never add the three voltages as plain numbers.
Resistors stay in step, capacitors lead current by a quarter cycle, inductors lag it, and phasor arrows add the three voltages into Z and phi.
2 · Watch
Take it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.