University of Waterloo Department of Electrical and Computer Engineering

GENE 123: Electrical Engineering

Mid-Term Exam W’03 February 07, 2003

Time Allowed: 2 Hours Instructor: David Brush

Instructions:

1. Answer all questions. 2. The exam is a closed book examination. 3. Electronic calculators are allowed. 4. Aid Sheet is attached at the end of the examination paper. 5. Clearly show all steps used in solution. No marks will be given for numerical

results unless accompanied with correct solution method. 6. Use correct SI units in all your answers,

Question Q1 Q2 Q3 Q4 Q5 Q6

Mark

Name:

I.D.#:

Question 1 page 2/10 Two point charges q1 = Q C and q2 = 4 Q C are located along the x-axis at (0,0) and (3,0) respectively as shown in figure 1.

(a) Calculate the magnitude and direction of the electric

field vector at (1,0). (b) Find the location, magnitude and sign of a third point

charge so that the entire system of charges is in equilibrium. (Net force acting on each charge =0)

Figure 1

Question 2 page 3/10 Three point charges are placed at the three corners of a right angle triangle as shown in Figure 2. Calculate: (a) The potential at the point marked p. (b) The potential energy of q1

q1= 5q

q2= - 3q

--

+

q3= - 3q

d = 0.05mp

d

Figure 2

Question 3 page 4/10 A straight piece of wire (mass = 10.5 g, length = 50 cm) rests on top of two rails and completes the circuit shown in figure 3. A uniform magnetic field of 0.206 T acts parallel to the rails (into the page) and perpendicular to the wire. (a) What is the value of i just before the wire lifts off the rails? (b) Will the wire levitate if the magnitude of i is increased?

50 cmLeft Rail Right Rail

10.5 g section of wire

0.206 T (into page)

i Figure 3

Question 4 page 5/10 Figure 4 shows an electric circuit that comprises a 36V Voltage source, a dependent source and three resistors R1= 3 ohms, R3=14 ohms and R2 (unknown). (a) Compute the power supplied or absorbed by each

source. (b) Apply the power balance equation (∑ Power supplied =

∑ Power absorbed) to determine the magnitude and direction of the current through element 2.

(c) What is the value of R2?

Figure 4

Question 5 page 6/10 (a) Find i in the network shown in figure 5 using KCL.

4 Ω

+

12 V

−

3 Ω4 Ω

2 Ω

2 Ω12 A

2 A

i

Figure 5

page 7/10 (b) Find v in the network shown in figure 6 using KCL & KVL.

Figure 6

Question 6 page 8/10 (a) Find: RAB of the resistive network shown in Figure 7.

R1= 1kΩ

B

R ABR2= 1kΩ

R 3= 1

k Ω

R 7= 1kΩ

R4=

1kΩ

R 5= 1kΩ

R6= 1kΩ

A

Figure 7

page 9/10

(b) Find Vo across R3 for the resistive network shown in Figure 8.

Is = 24mA

Vo

+

-

R1= 6kΩ

R2= 3kΩ

R3= 3kΩ

R4= 6kΩ

Figure 8

page 10/10 Formula Sheet: (Winter 2003) ME123 & GENE123

19

212

0 2

70 2

1.602192 10 [ ]

8,85419 10 [ ]

4 10

1. Constan

t

[

s

e C

C

N mN

A

ε

µ π

−

−

−

= − ×

= ×⋅

= ×

1 212 2

0 12 1

20

0

2Coulomb's Law [ N]

4

N [ ]C

NPoint Charge [ ]

C4

[ V]

2. Electrostatic

(Zero Voltage at )4

.

Field

pp

P

f

f ii

q qF

r

FEq

qE

r

qV

r

V V E ds

rπε

πε

πε

∧⋅=

=

=

= ∞

− = − ∫

urr

ur uur [V]

[3. Magn

Netic Fiel

]

[

d

N]v

i

Magentic Forceon particleinmotion F qv B

Magentic Forceoncurrent carryingwire F iL B

= ×= ×

1 2

1 2

[V]

Re : ( ) ...

Re :1/ 1 / 1 / ...1/

tan ( ) 1 / ( )

( ) [W]

dW dq.

4. Ohms

dq dtdd

a

Wt

L w

s N

p N

V I Ristors inseries R R R R

istors in parallel R R R R

Conduc ce G R

Power WattP V I

= ⋅Ω = + +

= + +

= Ω

= ⋅

=

=

J

2

2

in .

in /

Also terms of current P I R

And terms of voltage P V R

=

=