Alternating Current
Alternating current (AC) is an electric current that periodically reverses direction, in contrast to direct current which flows only in one direction. The magnitude and direction of AC vary sinusoidally with time at a specific frequency — 50 Hz in India and most of the world, 60 Hz in North America. AC is the standard form of electrical power delivered to homes and industries because it can be efficiently stepped up or down in voltage using transformers, making long-distance transmission economical.
Key Formula
i(t) = I₀ × sin(ωt + φ)
LaTeX: i(t) = I_0 \sin(\omega t + \phi)
| Symbol | Meaning | Unit |
|---|---|---|
| i(t) | Instantaneous current at time t | Ampere (A) |
| I₀ | Peak (maximum) current amplitude | Ampere (A) |
| ω | Angular frequency (ω = 2πf) | Radians per second (rad/s) |
| t | Time | Second (s) |
| φ | Initial phase angle | Radians |
Worked Example
Problem
An AC supply has a peak voltage of 325 V at a frequency of 50 Hz. Write the expression for the instantaneous voltage as a function of time and find the voltage at t = 0.005 s.
Solution
Step 1: Write the general expression for AC voltage. v(t) = V₀ sin(ωt) (assuming phase φ = 0) Step 2: Calculate angular frequency. ω = 2πf = 2π × 50 = 314.16 rad/s Step 3: Expression for instantaneous voltage. v(t) = 325 sin(314.16 t) volts Step 4: Find voltage at t = 0.005 s. v(0.005) = 325 × sin(314.16 × 0.005) v(0.005) = 325 × sin(1.5708) v(0.005) = 325 × sin(π/2) v(0.005) = 325 × 1 = 325 V
Answer
v(t) = 325 sin(314.16 t) V; at t = 0.005 s, v = 325 V (peak value)
Key Parameters of Standard AC Supplies in India
| Parameter | Single Phase (Domestic) | Three Phase (Industrial) | Unit |
|---|---|---|---|
| RMS Voltage | 230 | 415 | V |
| Peak Voltage | 325 | 587 | V |
| Frequency | 50 | 50 | Hz |
| Angular Frequency | 314.16 | 314.16 | rad/s |
| Period | 0.02 | 0.02 | s |
| Phase Difference (between phases) | N/A | 120 | ° |
Interactive Tools
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Related Terms
RMS Voltage
RMS (Root Mean Square) voltage is the effective value of an alternating voltage, defined as the square root of the mean of the squares of all instantaneous voltage values over one complete cycle. It represents the equivalent DC voltage that would deliver the same power to a resistive load as the AC voltage. For a sinusoidal AC supply, the RMS voltage equals the peak voltage divided by √2, which is why the 230 V delivered to Indian homes corresponds to a peak voltage of approximately 325 V.
Direct Current
Direct current (DC) is an electric current that flows consistently in one direction, with charge carriers (typically electrons) moving from the negative terminal to the positive terminal of a source. Unlike alternating current, the magnitude of DC does not periodically reverse; it may be steady or vary in magnitude but never changes polarity. DC is produced by batteries, fuel cells, solar cells, and rectifiers, and is essential in electronics, mobile devices, electric vehicles, and renewable energy storage systems.
Electromagnetic Induction
Electromagnetic induction is the process by which a changing magnetic field within a closed conductor induces an electromotive force (EMF) and consequently an electric current in the conductor. Discovered by Michael Faraday in 1831, it is governed by Faraday's Law and Lenz's Law, and forms the operational basis of virtually all large-scale electrical power generation, transformers, and countless sensing devices. The phenomenon demonstrates the deep relationship between electricity and magnetism, first unified in Maxwell's equations.
"Alternating" from Latin "alternare" meaning "to do by turns", from "alternus" (every other). "Current" from Latin "currens" meaning "running" or "flowing". The term came into widespread use with the AC vs DC "War of Currents" debates of the 1880s between Tesla and Edison.