Higher Engineering Mathematics, Sixth Edition

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=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]

2. 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]


3. 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]