lagging

lagging

1. What Lagging Means (phase)

Lagging = one sinusoid peaks later than the reference. If $v(t)=V_m sin(ωt)$ and $i(t)=I_m sin(ωt - θ)$ where $θ>0$, then $i$ lags $v$ by $θ$ (or $v$ leads $i$ by $θ$).

• Lagging angle positive: $i$ reaches peak $θ/ω$ seconds after $v$.
• In phasor diagram, lagging phasor is clockwise (negative angle) from reference.

2. Typical LG Cases in Circuits

Circuit	Relation	Lagging Quantity
Inductor (pure $L$)	$v = L di/dt$	$i$ lags $v$ by $90°$ (or $v$ leads $i$ 90°)
Series RL	$v$ leads $i$ by $φ= tan^{-1}(X_L/R)$	$i$ lags $v$ by $φ$ ($0<φ<90°$)
General inductive	$φ>0$	Current lagging indicates inductive (positive $X$)

3. Worked Illustration

(a) v=10 sin(314t) (reference 0°), i=5 sin(314t -60°) ⇒ i lags v by 60° (or v leads i 60°) ⇒ power factor cos60°=0.5 lagging.

(b) Pure inductor: v=Vm sinωt, i=Im sin(ωt-90°) ⇒ lagging 90° ✓

(c) Need to say "lagging power factor" means current lags voltage (inductive load like motor).

4. Exam Points

• Define lagging as "peaks later, phase -θ" — 3-5 marks, frequent.
• Show $i$ lags $v$ by $θ$ means $i=I_m sin(ωt-θ)$ — 3 marks, frequent.
• Give inductor example $i$ lags $v$ $90°$ — 5 marks, very frequent (common lagging example).
• Distinguish from leading — 3 marks.