AC Circuits Explained — Pure R, L, C, Series & Parallel Combinations Compared

Alternating current (AC) circuit analysis is one of the most heavily tested topics across ECET, GATE (EC/EE), diploma and B.Tech semester exams — and it's also where most students lose easy marks, simply because the phase relationship between voltage and current is never revised side-by-side for every circuit type. In this article we compare all the fundamental AC circuits — Pure R, Pure L, Pure C, and their series and parallel combinations — in one place, with the waveform and phasor picture for each.

Poster Cover — AC Fundamentals & Quick Reference

Poster front and back cover: AC fundamentals, phasor representation, complex impedance, R-L-C series impedance triangle, formula summary, series and parallel circuit comparison tables, and exam tips quick recap — Cover — AC fundamentals, phasor theory, the R-L-C impedance triangle, formula summary, and the two comparison tables and exam tips reproduced as text below.

Part 1 — Circuit, Waveform & Phasor Diagrams for All 9 Circuits

Comparison poster of nine AC circuit types — Pure R, Pure L, Pure C, R-L series, R-C series, R-L-C series, R-L parallel, R-C parallel and R-L-C parallel — with circuit diagram, waveform and phasor diagram for each — Part 1 — circuit diagram, voltage/current waveform and phasor diagram side by side for all nine circuits.

Part 2 — Instantaneous Power, Derivations & Exam Tips for All 9 Circuits

Instantaneous power waveforms and derivation of average power, with exam tips, for all nine AC circuit types — Part 2 — instantaneous power waveform (p = vi), step-by-step derivation of average power, and a one-line exam tip for each circuit.

Comparison Table — Series Circuits

Circuit	Impedance Z	Phase angle φ	Current i	cos φ	Avg. Power P
R	R	0	in phase with v	1	VI
L	X_L	+90°	lags v by 90°	0	0
C	X_C	−90°	leads v by 90°	0	0
R-L	√(R²+X_L²)	tan⁻¹(X_L/R)	lags v by φ	R/Z	VI cos φ
R-C	√(R²+X_C²)	tan⁻¹(X_C/R)	leads v by φ	R/Z	VI cos φ
R-L-C	√(R²+(X_L−X_C)²)	tan⁻¹((X_L−X_C)/R)	lags/leads by φ	R/Z	VI cos φ

Comparison Table — Parallel Circuits

Circuit	Admittance Y = 1/Z	Phase angle φ	Current I	cos φ	Avg. Power P
R-L	√(G²+B_L²)	tan⁻¹(I_L/I_R)	lags V by φ	I_R/I	V²/R
R-C	√(G²+B_C²)	tan⁻¹(I_C/I_R)	leads V by φ	I_R/I	V²/R
R-L-C	√(G²+(B_C−B_L)²)	tan⁻¹((I_L−I_C)/I_R)	lags/leads by φ	I_R/I	V²/R

G = 1/R (conductance); B_L = 1/X_L, B_C = 1/X_C (susceptances)

Exam Tips — Quick Recap (All 9 Circuits)

R: v, i in phase; instantaneous power never goes negative.
L: field stores and returns energy every half-cycle; net power is zero.
C: dielectric stores and returns energy every half-cycle; net power is zero.
R-L: lagging power factor — typical of motors, chokes and transformers.
R-C: leading power factor — used in filters and phase-shifting networks.
R-L-C: X_L = X_C ⇒ resonance, unity p.f., circuit behaves as purely resistive.
R-L Parallel: V is the common reference (not I); I lags V — lagging p.f., same as series R-L.
R-C Parallel: V is the common reference (not I); I leads V — leading p.f., same as series R-C.
R-L-C Parallel: I_L = I_C ⇒ PARALLEL resonance — I is MIN, Z is MAX: opposite of series resonance.

Conclusion

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