Question

Two a.c V1=100sin(wt) and V2 = 150cos(wt) are fed into one circuit, determine the combined output of the two as a single a.c

Answer 1

Answer:

Explanation:

V = 100sin(ωt) + 150cos(ωt)

let x = ωt

V = 100sin(x) + 150cos(x)

a maximum or minimum will occur when the derivative is zero

V' = 100cos(x) - 150sin(x)

0 = 100cos(x) - 150sin(x)

100cos(x) = 150sin(x)

100/150 = sin(x)/cos(x)

0.6667 = tan(x)

x = 0.588 rad

V = 100sin(0.588) + 150cos(0.588)

V = 180.27756

as the maximum will not occur until ωt = 0.588 radians, for a cosine function we subtract that amount as a phase angle φ

V = 180.3 cos(ωt - 0.588)

or as a sine function, the phase angle lags the cosine by a difference of π/2

V = 180.3sin(ωt - (0.588 - π/2)

V = 180.3sin(ωt + 0.983)