AC through Capacitor
I leads V by 90°. X_C = 1/(ωC) falls with frequency.
Key Notes
A pure capacitor lets the current jump first, voltage builds up. Driven by v = V₀ sin(ωt), current is i = (V₀/X_C) sin(ωt + π/2).
Current LEADS voltage by 90°. When V is zero (about to rise), I is at its peak.
Capacitive reactance: X_C = 1/(ωC) = 1/(2πfC). Units: Ω. FALLS with frequency.
At DC (f = 0): X_C → ∞ (capacitor BLOCKS DC after charging). At very high f: X_C → 0 (capacitor passes AC like a wire).
Average power: P_avg = 0 (cos(π/2) = 0). Like an inductor, no net energy dissipation.
Phasor: I leads V by 90° — current phasor is 90° counter-clockwise from voltage phasor.
Capacitors store energy in the electric field — energy goes back and forth between source and capacitor.
Formulas
Capacitive reactance
Falls hyperbolically with f.
Peak / rms current
Ohm-like relation.
Current waveform
Leads voltage by 90°.
Average power
Wattless capacitor.
Instantaneous power
Oscillates at 2ω; averages to zero.
Important Points
Mnemonic ELI the ICE man: in capacitor (C) I leads voltage (E), in inductor (L) voltage (E) leads I.
X_C is a function of frequency — same capacitor 'looks smaller' at higher f.
Capacitors are open-circuit at DC (block), short-circuit at high frequency (pass).
Capacitors are used to BLOCK DC while passing AC (coupling capacitors in amplifiers).
Capacitors and inductors are duals: X_L ∝ f, X_C ∝ 1/f. Their reactances cancel at resonance ω₀ = 1/√(LC).
Capacitors and inductors store / return energy without loss — only resistors dissipate.
AC through Capacitor notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.