The complex or exponential form of a Fourier series 657
Now try the following exercise
Exercise 238 Further problems on phasors
- Determine the pair of phasors that can be used
to represent the following voltages:
(a)v=4cos4t (b)v=4cos( 4 t+π/ 2 ).
[(a) 2ej^4 t+2e−j^4 t, 2 ∠ 0 ◦ anticlock-
wise, 2∠ 0 ◦ clockwise, each with
ω=4rad/s
(b)2ej^4 tejπ/^2 +2e−j^4 te−jπ/^2 , 2 ∠π/ 2
anticlockwise, 2∠−π/2clockwise,
each withω=4rad/s]
- Determine the pair of phasors that can repre-
sent the harmonic given by:
v=10cos2t−12sin2t.
[( 5 +j 6 )ej^2 t+( 5 −j 6 )e−j^2 t,
7. 81 ∠ 0 .88 rotating anticlockwise,
7. 81 ∠− 0 .88 rotating clockwise, each
withω=2rad/s] - Find the pair of phasors that can represent the
fundamental current:i=6sint+4cost.
[( 2 −j 3 )ejt+( 2 +j 3 )e−jt,
3. 61 ∠− 0 .98 rotating anticlockwise,
3. 61 ∠ 0 .98 rotating clockwise, each
withω=1rad/s]