Alternating Current (AC) – Class 12 (CBSE)
(Physics – 12th Grade – 2026)
1. Introduction – What is Alternating Current?
- Alternating Current (AC) is a current whose magnitude and direction change periodically with time.
- In contrast, Direct Current (DC) flows only in one direction.
- AC is used for almost all electricity that reaches homes, industries, and electronics because it can be easily transformed to different voltages and transmitted over long distances.
Simple explanation
Imagine a water pipe that alternates between pushing water forward and backward. That’s AC – the flow direction keeps switching.
2. Key Concepts & Definitions
| Term | Definition | Symbol | Formula (if applicable) |
|---|---|---|---|
| Frequency (f) | Number of complete cycles per second | f | 1/T |
| Period (T) | Time for one complete cycle | T | 1/f |
| Peak (Vₘ) | Maximum instantaneous value of voltage/current | Vₘ | |
| RMS (Root‑Mean‑Square) | Equivalent DC value that delivers the same power | V₍rms₎ | (V_{\text{rms}} = \dfrac{V_{\text{m}}}{\sqrt{2}}) |
| Phase Angle (ϕ) | Shift between voltage and current in AC circuits | ϕ | |
| Impedance (Z) | Total opposition to AC flow (resistance + reactance) | Z | (Z = \sqrt{R^{2} + X^{2}}) |
| Reactance (X) | Opposition due to inductors (XL) or capacitors (XC) | X | (X_L = 2\pi fL), (X_C = \dfrac{1}{2\pi fC}) |
| Power factor (PF) | Cosine of phase angle – indicates how effectively power is used | PF | (\cos \phi) |
| Average Power (P) | Time‑averaged power in AC | P | (P = V_{\text{rms}} I_{\text{rms}} \cos \phi) |
3. AC Waveforms
| Waveform | Equation (instantaneous) | Peak to RMS | Notes |
|---|---|---|---|
| Sinusoidal | (V(t) = V_{\text{m}}\sin(2\pi f t)) | (V_{\text{rms}} = V_{\text{m}}/\sqrt{2}) | Most common |
| Square | (V(t) = V_{\text{m}}) for half cycle, (-V_{\text{m}}) for the other | (V_{\text{rms}} = V_{\text{m}}) | Used in switching devices |
| Triangular | Linear rise/fall | (V_{\text{rms}} = V_{\text{m}}/\sqrt{3}) | Used in signal generators |
| Saw‑tooth | Linear rise, sudden drop | (V_{\text{rms}} = V_{\text{m}}/\sqrt{3}) | Used in oscilloscopes |
Tip: In exams, most problems use sinusoidal AC because of its mathematical simplicity.
4. AC Generation & Transmission
-
Generation –
- Synchronous generators (alternators) convert mechanical rotation into AC.
- Rotating magnetic field produces sinusoidal output.
-
Step‑Up & Step‑Down –
- Transformer: Uses mutual induction; (V_{\text{out}}/V_{\text{in}} = N_{\text{out}}/N_{\text{in}}).
- Purpose: Increase voltage for long‑distance transmission (reduces current → lowers I²R losses).
-
Transmission –
- High‑voltage AC (e.g., 400 kV) is transmitted.
- At the destination, voltage is stepped down to usable levels.
5. AC Circuits – Resistive, Inductive, Capacitive
| Type | Impedance | Current‑Voltage Relationship | Power Factor |
|---|---|---|---|
| Resistive (R) | (Z = R) | In‑phase | 1 |
| Inductive (L) | (Z = R + jX_L) | Current lags voltage by 90° | 0 (purely reactive) |
| Capacitive (C) | (Z = R - jX_C) | Current leads voltage by 90° | 0 (purely reactive) |
| R–L or R–C | (Z = R + j(X_L - X_C)) | Phase shift depends on net reactance | (\cos \phi) |
Key: In power systems, the power factor is usually > 0.8 to ensure efficient power transfer.
6. Power in AC Circuits
| Quantity | Symbol | Formula | Meaning |
|---|---|---|---|
| Mean power | P | (P = V_{\text{rms}} I_{\text{rms}} \cos \phi) | Average power delivered |
| Apparent power | S | (S = V_{\text{rms}} I_{\text{rms}}) | Product of rms voltage & current |
| Reactive power | Q | (Q = V_{\text{rms}} I_{\text{rms}} \sin \phi) | Power stored & released by reactances |
- Power triangle: (S^2 = P^2 + Q^2).
7. Worked Example
Problem
A 220 V (rms) AC supply at 50 Hz powers a circuit consisting of a 10 Ω resistor and a 100 µH inductor in series.
- Find the rms current.
- Calculate the mean power consumed.
- Determine the