7b Calculating the phase angle between voltage and current

A recurring calculation asks specifically for the phase difference (not just the impedance) and which quantity leads — worth its own worked method rather than folding it into the reactance formulas.

The phase angle in a series RLC circuit

Phase angle \tan\varphi=\frac{X_L-X_C}{R} φ is the angle by which the supply voltage leads (or lags) the current. Which one leads X_L > X_C → voltage leads current (inductive circuit). X_C > X_L → current leads voltage (capacitive circuit). If X_L = X_C exactly, φ = 0: voltage and current are in phase — this is resonance. Real paper — 2024 Calculating the phase difference in an inductor-and-bulb circuit A 70.0 mH inductor (reactance shown to be 26.4 Ω) is in series with a 40.0 Ω bulb on a 110 V RMS, 60.0 Hz supply. Calculate the phase difference between the supply voltage and the circuit current, and state which one leads. This circuit has no capacitor, so X_C = 0: tan φ = (X_L − 0) / R = 26.4 / 40.0 = 0.660. φ = tan⁻¹(0.660) = 33.4° (0.583 rad). Since X_L > X_C (and there is inductance but no capacitance), the circuit is inductive, so the supply VOLTAGE leads the current by 33.4°. ✓ φ ≈ 33.4° (the 2024 schedule rounds it to 33°), voltage leading — matching the "ELI" mnemonic (voltage leads current in an inductor). ✕

Forgetting to state WHICH quantity leads

Calculating φ correctly but not stating whether voltage leads current (or vice versa) leaves the answer incomplete — the schedule asks for both the SIZE of the phase difference and its DIRECTION. Check whether X_L or X_C dominates to decide which leads, using ELI the ICE man as a quick sanity check.

Practice for this standard covers the whole topic — flashcards and quiz.