leading

leading

1. What Leading Means (phase)

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

• Leading angle positive: $i$ peaks $θ/ω$ seconds before $v$.
• In phasor diagram, leading phasor is counter-clockwise (positive angle) from reference.

2. Typical Leading Cases in Circuits

Circuit	Relation	Leading Quantity
Capacitor (pure $C$)	$i = C dv/dt$	$i$ leads $v$ by $90°$ (or $v$ lags $i$ 90°)
Series RC	$v$ lags $i$ by $φ= tan^{-1}(X_C/R)$? Actually $i$ leads $v$ by $φ$ where $tan φ = X_C/R$	$i$ leads $v$ ($0<φ<90°$)
General capacitive	$φ<0$ (if $v$ reference)	Current leading indicates capacitive (negative $X$)

3. Worked Illustration

(a) v=10 sin(314t) (0°), i=5 sin(314t+45°) ⇒ i leads v by 45° ⇒ power factor cos45°=0.707 leading (capacitive).

(b) Pure capacitor: v=Vm sinωt, i=Im sin(ωt+90°) ⇒ leading 90° ✓

(c) Need to say "leading power factor" means current leads voltage (capacitive load like capacitor bank).

(d) Leading vs lagging determines whether to add capacitor to correct power factor (lagging inductive load compensated by leading capacitor).

4. Exam Points

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