Revision Test 7
This Revision Test covers the material contained in Chapters 20 to 23.The marks for each question are shown in
brackets at the end of each question.
- Solve the quadratic equationx^2 − 2 x+ 5 =0and
showtherootsonanArganddiagram. (9) - IfZ 1 = 2 +j5,Z 2 = 1 −j3andZ 3 = 4 −jdeter-
mine, in both Cartesian and polar forms, the value
of
Z 1 Z 2
Z 1 +Z 2+Z 3 , correct to 2 decimal places.
(9)- Three vectors are represented byA,4. 2 ∠ 45 ◦,B,
5. 5 ∠− 32 ◦andC, 2. 8 ∠ 75 ◦. Determine in polar
form the resultantD,whereD=B+C−A.(8) - Two impedances, Z 1 =( 2 +j 7 ) ohms and
Z 2 =( 3 −j 4 )ohms, are connected in series to
a supply voltage V of 150∠ 0 ◦V. Determine the
magnitude of the currentIand its phase angle
relative to the voltage. (6) - Determine in both polar and rectangular forms:
(a) [2. 37 ∠ 35 ◦]^4 (b) [3. 2 −j 4 .8]^5
(c)
√
[− 1 −j3] (15)In questions 6 to 10, the matrices stated are:
A=(
− 52
7 − 8)
B=(
16
− 3 − 4)C=(
j 3 ( 1 +j 2 )
(− 1 −j 4 ) −j 2)D=⎛
⎝2 − 13
− 510
4 − 62⎞
⎠ E=⎛
⎝− 130
4 − 92
− 571⎞
⎠- DetermineA×B.(4)
- Calculate the determinant of matrixC.(4)
- Determine the inverse of matrixA.(4)
- DetermineE×D.(9)
- Calculate the determinant of matrixD.(6)
- Solve the following simultaneous equations:
4 x− 3 y= 17
x+y+ 1 = 0using matrices. (6)- Use determinants to solve the following simulta-
neous equations:
4 x+ 9 y+ 2 z= 21
− 8 x+ 6 y− 3 z= 41
3 x+y− 5 z=− 73 (10)- The simultaneous equations representing the cur-
rents flowing in an unbalanced, three-phase, star-
connected, electrical network are as follows:
2. 4 I 1 + 3. 6 I 2 + 4. 8 I 3 = 1. 2
− 3. 9 I 1 + 1. 3 I 2 − 6. 5 I 3 = 2. 6
1. 7 I 1 + 11. 9 I 2 + 8. 5 I 3 = 0Using matrices, solve the equations for I 1 , I 2
andI 3. (10)