The complex or exponential form of a Fourier series 657
Now try the following exercise
Exercise 238 Further problems on phasors
1. Determine the pair of phasors that can be used
to represent the following voltages:
(a) v = 4 cos4t (b) v = 4 cos(4t + π/2).
[(a) 2e j 4t + 2e − j 4t , 2∠0 ◦ anticlockwise, 2∠0 ◦ clockwise, each with
ω = 4 rad/s
(b) 2e j 4t e j π/2 + 2 e − j 4t e − j π/2 , 2∠π/2
anticlockwise, 2∠ −π/2 clockwise,
each with ω = 4 rad/s]
2. Determine the pair of phasors that can represent the harmonic given by:
v = 10 cos 2t − 12 sin 2t .
[(5 + j 6)e j 2t + (5 − j 6)e − j 2t ,
7.81∠0.88 rotating anticlockwise,
7.81 ∠−0.88 rotating clockwise, each
with ω = 2 rad/s]
3. Find the pair of phasors that can represent the
fundamental current: i = 6 sint + 4 cost .
[(2 − j 3) e jt + (2 + j 3) e − jt ,
3.61∠−0.98 rotating anticlockwise,
3.61 ∠ 0.98 rotating clockwise, each
with ω = 1 rad/s]