Higher Engineering Mathematics

THE COMPLEX OR EXPONENTIAL FORM OF A FOURIER SERIES 703

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Now try the following exercise.

Exercise 250 Further problems on phasors

1. Determine the pair of phasors that can be used
   to represent the following voltages:
   (a)v=4 cos 4t (b)v=4 cos (4t+π/2)

[(a) 2ej^4 t+2e−j^4 t,2∠ 0 ◦ anticlockwise,

2 ∠ 0 ◦clockwise, each withω=4 rad/s

(b) 2ej^4 tejπ/^2 +2e−j^4 te−jπ/^2 ,2∠π/ 2

anticlockwise, 2∠−π/2 clockwise, each

withω=4 rad/s]

2. Determine the pair of phasors that can repre-
   sent the harmonic given by:
   v=10 cos 2t−12 sin 2t

[(5+j6)ej^2 t+(5−j6)e−j^2 t,7. 81 ∠ 0. 88

rotating anticlockwise, 7. 81 ∠− 0. 88

rotating clockwise, each withω=2 rad/s]

3. Find the pair of phasors that can represent the
   fundamental current:i=6 sint+4 cost

[(2−j3) ejt+( 2 +j 3 )e−jt,3. 61 ∠− 0. 98

rotating anticlockwise, 3. 61 ∠ 0 .98 rotat-

ing clockwise, each withω=1 rad/s]