ABSTRACT
Plot the two voltages on the same axes to scales of 1cm=50 volts and 1cm= π
6 rad. Obtain a sinu-
soidal expression for the resultant υ1 +υ2 in the form R sin(ωt+α): (a) by adding ordinates at intervals and (b) by calculation (13)
5. If velocity v1 = 26m/s at 52◦ and v2 = 17m/s at −28◦ calculate the magnitude and direction of v1 + v2, correct to 2 decimal places, using complex numbers (10)
6. Given a = −3i+ 3j + 5k, b = 2i− 5j + 7k and c = 3i+ 6j − 4k, determine the following: (i) −4b (ii) a+ b− c (iii) 5b− 3c (8)
7. Solve the quadratic equation x2 −2x+5=0 and show the roots on an Argand diagram (8)
8. If Z1 =2+ j5, Z2 =1− j3 and Z3=4− j determine, in both Cartesian and polar forms, the value of:
Z1Z2 Z1+ Z2 + Z3, correct to 2 decimal places (8)
9. Three vectors are represented by A, 4.2∠45◦, B, 5.5∠− 32◦ and C, 2.8∠75◦. Determine in polar form the resultant D, where D = B+C –A (8)
10. Two impedances, Z1 = (2+ j7) ohms and Z2 = (3+ j4) ohms are connected in series to a supply voltage V of 150∠0◦V. Determine the magnitude of the current I and its phase angle relative to the voltage (6)
11. Determine in both polar and rectangular forms: (a) [2.37∠35◦]4 (b) [3.2− j4.8]5 (c) √−1− j3
(15)
