Class 12 Physics - AC Circuits (Complete Theory)

Alternating Current (AC) Circuit

1. Difference Between AC and DC

Direct Current (DC) flows in one direction only. Example: Battery current.

Alternating Current (AC) changes direction periodically. In India, AC has a frequency of 50 Hz.

  • DC: Constant magnitude and direction
  • AC: Varies sinusoidally with time

2. Mathematical Expression of AC

An AC voltage or current can be expressed as:

v(t) = V₀ sin(ωt + φ)

  • V₀: Peak voltage
  • ω: Angular frequency = 2πf
  • φ: Phase constant

Similarly, current: i(t) = I₀ sin(ωt + φ)

3. AC Through Resistor, Inductor, and Capacitor

Resistor Only (R):

Voltage and current are in phase.

Inductor Only (L):

Current lags voltage by 90°. Inductive reactance: XL = ωL

Capacitor Only (C):

Current leads voltage by 90°. Capacitive reactance: XC = 1/ωC

Phase Relations: Resistor (R): V(t): ~~~~~~~ I(t): ~~~~~~~ (in phase) Inductor (L): V(t): ~~~~~~~ I(t): ~~~~~~~ (lags) Capacitor (C): I(t): ~~~~~~~ V(t): ~~~~~~~ (lags)

4. Impedance and Reactance

Reactance is the opposition offered by inductors and capacitors to AC:

  • Inductive Reactance: XL = ωL
  • Capacitive Reactance: XC = 1/ωC

Impedance (Z) is the total opposition in an AC circuit:

Z = √(R² + (XL - XC)²)

5. LCR Series Circuit

An LCR circuit has a Resistor (R), Inductor (L), and Capacitor (C) in series.

The net voltage is the vector sum of voltages across each component.

Impedance: Z = √(R² + (XL - XC)²)

Current: I = V / Z

Phasor Diagram (when XL > XC): | (VL) | ---+----------→ (VR) | | (VC)

6. Power in AC Circuit

Power in AC is not constant. Average power is given by:

P = Vrms × Irms × cos(ϕ)

  • cos(ϕ) is called the Power Factor
  • If ϕ = 0 (pure resistor), power is maximum
  • If ϕ = 90° (pure inductor/capacitor), average power = 0

7. Resonance in LCR Circuit

Resonance occurs when:

XL = XC

At resonance:

  • Impedance Z = R (minimum)
  • Current is maximum: I = V / R

Resonant frequency: fr = 1 / (2π√(LC))

8. Transformer

A transformer changes the voltage of AC using electromagnetic induction.

It has two coils: Primary and Secondary, wound on an iron core.

Equation:

Vs / Vp = Ns / Np

  • Step-up: Increases voltage (Ns > Np)
  • Step-down: Decreases voltage (Ns < Np)

9. Why AC is Preferred Over DC?

  • AC can be easily stepped up or down using transformers.
  • AC transmission over long distances is more economical (less energy loss).
  • DC requires expensive conversion equipment.

10. Applications of AC Circuits

  • Household electricity (220V, 50Hz AC)
  • Electric fans, tube lights, refrigerators, etc.
  • AC motors used in industries
  • Transformers in substations
AC circuit