1. What is Alternating Current (AC)?
Alternating Current (AC) is an electric current that changes magnitude and direction periodically. In AC, electrons oscillate back and forth. A common example is household power supply, which is 50 Hz in India.
Network Analysis
AC Fundamentals - Complete Theory Guide
This page explains alternating current, sinusoidal quantities, RMS and average values, phase, reactance, impedance, AC power, power factor, resonance, and phasor representation in one clean sequence.
2. Basic AC Quantities
2.1 Instantaneous Value
v(t) = Vm sin(omega t + phi)
- Vm is the maximum or peak voltage.
- omega is angular frequency in rad/s.
- phi is the phase angle.
- t is time.
2.2 Angular Frequency
omega = 2 pi f
- f is frequency in hertz.
2.3 Time Period
T = 1 / f
- T is the time taken to complete one full cycle.
2.4 Frequency
f = cycles per second
- Frequency is measured in hertz (Hz).
3. RMS, Average, and Peak Values
3.1 RMS Value (Root Mean Square)
Vrms = Vm / sqrt(2)
Equivalent DC value producing the same power.
3.2 Average Value
Vavg = 2Vm / pi
For half-cycle only.
3.3 Form Factor
Form Factor = Vrms / Vavg = 1.11
It compares heating value with average rectified value.
4. Phase and Phase Difference
Phase indicates the position of a waveform in time. Phase difference occurs when two waves are shifted from each other.
- In phase means both waveforms match.
- Leading means one waveform is ahead.
- Lagging means one waveform is behind.
5. AC Circuit Elements
5.1 Pure Resistive Circuit
- Voltage and current are in phase.
- The resistor does not create phase shift.
V = IR
5.2 Pure Inductive Circuit
- Current lags voltage by 90 deg.
- Inductive reactance increases with frequency.
XL = omega L, V = IXL
5.3 Pure Capacitive Circuit
- Current leads voltage by 90 deg.
- Capacitive reactance decreases as frequency increases.
XC = 1 / omega C
6. Impedance (Z)
Impedance is the total opposition offered by an AC circuit. It combines resistance and net reactance.
Z = sqrt(R^2 + (XL - XC)^2)
Unit: ohms.
7. Phase Angle
tan phi = (XL - XC) / R
8. AC Power
8.1 Instantaneous Power
p(t) = v(t) * i(t)
8.2 Average Power
P = Vrms Irms cos phi
8.3 Reactive Power
Q = Vrms Irms sin phi
8.4 Apparent Power
S = Vrms Irms
Power Triangle
9. Power Factor
Power Factor = cos phi
- Range: 0 to 1.
- High power factor means a more efficient system.
10. Types of AC Circuits
10.1 Series RLC Circuit
Z = R + j(XL - XC)
10.2 Resonance Condition
XL = XC
fr = 1 / (2 pi sqrt(LC))
- At resonance, impedance is minimum.
- At resonance, current is maximum.
11. Phasor Representation
- AC quantities are represented as rotating vectors.
- Phasors simplify sinusoidal circuit calculations.
12. Key Summary
- AC varies sinusoidally.
- RMS value is most practical.
- Reactance depends on frequency.
- Impedance combines resistance and reactance.
- Power factor is crucial for efficiency.
- Resonance is an important AC phenomenon.