In pure capacitor circuit, which quantity is leading

Question

Examoogle · Accepted Answer

Option A: Current

Explanation & Concepts:
In a purely capacitive AC circuit, the current leads the voltage by a phase angle of $90^\circ$ (or $\frac{\pi}{2}$ radians). This occurs because the capacitor opposes the change in voltage by drawing current ahead of the voltage cycle.

Working Principle: When an AC voltage $v(t) = V_m \sin(\omega t)$ is applied to a capacitor $C$, the current is given by $i = C \frac{dv}{dt}$. Differentiating the voltage results in $i(t) = \omega C V_m \cos(\omega t) = \omega C V_m \sin(\omega t + 90^\circ)$. Thus, the current wave attains its peak value a quarter-cycle before the voltage wave.

Key Formulas: $i(t) = C \frac{dv}{dt}$ — Instantaneous current-voltage relationship; $X_C = \frac{1}{2\pi fC}$ — Capacitive reactance

Key Points: Current leads voltage by $90^\circ$ in a pure capacitor.; The capacitor stores energy in an electric field.; Reactance $X_C$ decreases as frequency $f$ increases.; A pure capacitor consumes zero average power (active power is zero).

Advantages: Energy storage capability in electric fields; Used for power factor correction

Disadvantages: Infinite reactance at DC ($f=0$); Non-ideal capacitors have equivalent series resistance (ESR)

Applications: Filtering circuits; Coupling and decoupling in electronics

Additional Info: The memory trick 'ELI the ICE man' is commonly used: ICE implies in a Capacitor (C), Current (I) leads Voltage (E).. Option B is incorrect because voltage lags current in a capacitive circuit; voltage leads current only in an inductive circuit.

Answer: A is correct — In a pure capacitor circuit, the current leads the voltage by a phase angle of $90^\circ$.

Exam Tip: Remember 'ELI the ICE man': In Inductors (L), E leads I; in Capacitors (C), I leads E.

Examoogle · Answer

Option B: Voltage

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