AC Circuit Analysis - Complete Step-by-Step Guide

1. What is AC Circuit Analysis?

AC circuit analysis is the process of determining voltage, current, and power in sinusoidal circuits. Unlike DC, values change with time, phase relationships matter, and complex numbers make the solution easier.

• Voltages and currents are time-dependent.
• Phase relationships decide leading or lagging behavior.
• Phasors convert sinusoidal equations into algebra.

2. Sinusoidal Signals in AC Circuits

The general voltage or current equation is the foundation of AC analysis.

v(t) = Vm sin(omega t + phi)

• Vm is the peak value.
• omega = 2 pi f is angular frequency.
• phi is the phase angle.

3. Phasor Representation

A phasor represents a sinusoid as a complex number with magnitude and angle. It changes differential equations into simpler algebraic equations.

V = Vrms angle phi

4. Impedance (Z) - Core of AC Analysis

In AC circuits, resistance becomes impedance. Impedance combines ordinary resistance and frequency-dependent reactance.

Z = R + jX

5. AC Ohm's Law

AC Ohm's Law has the same shape as DC Ohm's Law, but voltage, current, and impedance are complex phasor quantities.

V = IZ

6. Basic AC Circuit Analysis

6.1 Pure Resistive Circuit

• Z = R
• Voltage and current are in phase.

I = V / R

6.2 Pure Inductive Circuit

• Z = jXL
• Current lags voltage by 90 deg.

I = V / XL

6.3 Pure Capacitive Circuit

• Z = -jXC
• Current leads voltage by 90 deg.

I = V / XC

7. Series RLC Circuit Analysis

8. Parallel RLC Circuit Analysis

Parallel AC circuits are usually solved using admittance because branch currents add naturally.

9. Power in AC Circuits

Power Triangle

10. Power Factor

cos phi = P / S

• Lagging power factor means an inductive load.
• Leading power factor means a capacitive load.
• Unity power factor means voltage and current are in phase.

11. Resonance in AC Circuits

XL = XC

fr = 1 / (2 pi sqrt(LC))

• At resonance, series impedance is minimum.
• Current is maximum in a series RLC circuit.
• Power factor becomes 1.

12. Step-by-Step Method to Solve AC Circuits

1. Step 1

   Convert sinusoidal sources into RMS phasors.

2. Step 2

   Replace R, L, and C by their impedance forms.

3. Step 3

   Apply Ohm's Law, KVL, KCL, nodal analysis, or mesh analysis.

4. Step 4

   Solve the equations using complex algebra.

5. Step 5

   Convert the result back to time domain only when the question asks for it.

R maps to R, L maps to j omega L, C maps to 1 / (j omega C)

v(t) = Vm sin(omega t + phi)

13. Key Concepts Summary

• AC analysis uses phasors and complex numbers.
• Impedance replaces resistance in sinusoidal steady state.
• Reactance depends on frequency.
• Phase angle decides leading, lagging, and power behavior.
• RLC circuits are the basis of practical AC networks.