Side-by-side comparison
| Parameter | AC | DC Circuit Analysis |
|---|---|---|
| Supply | Constant magnitude and polarity (e.g., 12 V battery) | Sinusoidal, varies with time: v(t) = V_m sin(ωt + φ) |
| Governing Variable | Resistance R in ohms | Impedance Z = R + jX in ohms (complex) |
| Capacitor Behavior | Open circuit (blocks DC at steady state) | X_C = 1/(ωC) = 1/(2π×50×C) at 50 Hz |
| Inductor Behavior | Short circuit (wire resistance only at steady state) | X_L = ωL = 2π×50×L at 50 Hz |
| Analysis Tool | KVL, KCL with real numbers | Phasor domain (complex algebra) or Laplace transform |
| Power | P = V × I = I²R (all real power, unity power factor) | P = VI cosφ (real), Q = VI sinφ (reactive), S = VI (apparent) |
| Power Factor | Always 1.0 (unity) | Between 0 and 1; lagging for inductive, leading for capacitive load |
| Frequency Effect | Frequency irrelevant — capacitors open, inductors short | Impedance and phase shift change with frequency |
Key differences
DC analysis uses only resistance and real arithmetic — a 10 Ω resistor and 12 V battery give 1.2 A, done. AC analysis at 50 Hz must account for reactance: a 100 mH inductor has X_L = 31.4 Ω, and a 100 µF capacitor has X_C = 31.8 Ω — both comparable to typical resistances. Complex impedance Z = R + j(X_L – X_C) determines both magnitude and phase of current. Power factor (cosφ) is unity for DC always; for an RL load at 50 Hz with R = 10 Ω and L = 50 mH, φ = arctan(15.7/10) ≈ 57°, giving power factor 0.54 lagging.
When to use AC
Use DC circuit analysis for battery-powered electronics, digital logic supply rails, and sensor biasing circuits — for example, calculating the base current of a BC547 transistor biased from a 9 V DC supply.
When to use DC Circuit Analysis
Use AC circuit analysis for any mains-powered load, power distribution system, or signal processing circuit — for example, finding the current and power factor of a 230 V, 50 Hz supply driving a 500 W induction motor modeled as a series RL circuit.
Recommendation
For exam problems, identify the supply type first. DC supply means use R only and real arithmetic. AC supply means use Z = R + jX, convert to phasors, and calculate real power as P = I²R (not I²Z). That one check prevents the most common error in network analysis papers.
Exam tip: Examiners test power triangle relationships in AC: real power P = S cosφ, reactive power Q = S sinφ, apparent power S = √(P² + Q²) — draw the triangle and label all three sides before calculating.
Interview tip: Interviewers at power utilities like BESCOM or NTPC ask for the definition of power factor and how to correct it — say: power factor = cosφ = P/S; correct a lagging industrial load by adding shunt capacitors to cancel inductive reactive power.