Alternating Current — Formula Sheet

I = I0 sin ωt

V = V0 sin ωt

V0 = NBAω

T = 2π/ω

f = ω/(2π) = 1/T

Im = (2/π)I0 = 0.637 I0

Irms = I0/√2 = 0.707 I0

Vrms = V0/√2 = 0.707 V0

Im = 0

Irms for i = a + b sin ωt = √(a^2 + b^2/2)

tan φ = (XL − XC)/R = (ωL − 1/ωC)/R

In pure resistor, current is in phase with voltage

In pure inductor, current lags voltage by 90°

In pure capacitor, current leads voltage by 90°

XL = ωL = 2πfL

XC = 1/ωC = 1/(2πfC)

Z = √(R^2 + (XL − XC)^2)

f0 = (1/2π)√(1/LC)

Q = (1/R)√(L/C)

The peak emf induced in a rotating coil is V0 = NBAω.

For sinusoidal AC, Irms = I0/√2.

For square wave AC, Irms = I0.

For triangular wave AC, Irms = I0/√3.