12.2 Alternating current. 2 hours. Alternating Current. The induced emf in a coil rotated within a uniform magnetic field is sinusoidal if the rotation is at constant speed.
Δ θ ÷ Δt = the angular velocity, w, in rad s-1 = 2 π f
θ = ωt = 2πft
ε = ω ×N×A×B ×sin(ωt) or ε = 2πf ×N×A×B × sin(2 π f t)
ε0 = ω NBA
ε = ε0 sin(ω t)
I = I0sin(ωt)
The r.m.s. value of the alternating current that produces the power is equal to the d.c. value of the direct current.
P = V0 sin(ωt) × I0 sin(ωt) = V0I0 sin2(ωt)
P = I 2ave × R = I02R sin2ωt
The value of sin2ωt will therefore vary between 0 and 1. Therefore its average value = (0 + 1) / 2 = 1/2
It can be seen that if Ns is greater than Np then the transformer is a step-up transformer. If the reverse occurs and Ns is less than Np it will be a step-down transformer.