AC

Alternating Current

Use: Notes + Revision

Alternating Current

Basics

i = I₀ sin(ωt)

v = V₀ sin(ωt)

Direction changes periodically
ω = 2πf
Time period: T = 1/f

Average & RMS

Values

Average over full cycle = 0
Half cycle average:

Iavg = 2I₀ / π

Irms = I₀ / √2

Vrms = V₀ / √2

Important Facts

AC Supply

AC meters measure RMS values
Domestic supply = 220V (RMS)
Peak voltage = 311V
Frequency = 50Hz

AC Power

Formula

P = Vrms Irms cosφ

cosφ = power factor
Max when cosφ = 1

Single Component Circuits

R / L / C

Resistor: V & I in phase, cosφ = 1
Inductor: current lags by 90°, power = 0
Capacitor: current leads by 90°, power = 0

Reactance

XL / XC

XL = ωL

XC = 1 / (ωC)

Both act like resistance

Impedance

Z

Z = √(R² + (XL − XC)²)

R-L Circuit

Series

Current lags voltage
tanφ = XL / R

R-C Circuit

Series

Current leads voltage
tanφ = XC / R

RLC Circuit

Complete

Z = √(R² + (XL − XC)²)
If XL > XC → current lags
If XC > XL → current leads

Resonance

Condition

ω₀ = 1 / √(LC)

XL = XC
Z = R (minimum)
Current maximum

Quality Factor

Q

Q = ω₀L / R

Higher Q → sharper resonance

Transformer

Device

Works on mutual induction
Vs/Vp = Ns/Np
Step-up & step-down types

Transformer Losses

Types

Copper loss (I²R)
Eddy current loss
Hysteresis loss
Minimised using laminations & soft iron