Name
University of Saskatchewan
EP 155 – Electric and Magnetic Circuits
Final Examination
April 26, 2002
Time: 2:00 – 5:00 pm
Student’s Name: (Print)
Student Number:
Section (circle): Section 2(1:00 – 2:30 pm) Section 4 (2:30 – 4:00 pm)
Instructors: J.E. Salt, A.V. Koustov, J.E. Morelli
Notes:
Write your name on each page in the space provided.
Please report your final answers in the spaces provided.
Please show your work in order to demonstrate that you understand the material.
If you run out of space, then clearly indicate that you are using the back of the page.
The value of each partial question is indicated in parenthesis.
One 8½´11 sheet of paper with notes on it is permitted.
The use of any handheld calculator is permitted.
Make sure that your exam contains 15 pages with 8 questions.
Useful Constants:
k = 9.0´109 Nm2C-2
e0 = 8.85418´10-12 Fm-1
m0 = 4p´10-7 Hm-1
Marks for the exam
(do not write in this space)
Q1:Q2:
Q3:
Q4:
Q5:
Q6:
Q7:
Q8:
Total:
1. Consider a system consisting of two charged particles in a plane as shown in Figure 1. Particle 1 has a net charge of Q1 = +1 mC and is located at (0 m, 8 m) i.e. x=0m, y=8m. Particle 2 has a net charge of Q2 = +2 mC and is located at (8 m, 0 m). Refer to Figure 1 when answering the following questions.
a. What is the magnitude and the direction of the force on a test charge of +0.04 mC located at (8 m, 8 m)?
(4 marks)
b. How much work is required to move the test charge from (8m, 8 m) to (8 m, 2 m) i.e. move it 6 m directly towards Q2?
(4 marks)
c. Is the point (8 m, 8 m) at a higher electric potential than the point (8 m, 2 m)?
(1 mark)
d. What is the electric potential at point (8 m, 2 m) with respect to point (8 m, 8 m)? Express your answer in units of volts.
(2 marks)
Figure 1
2. Given the following circuit diagrams:
Figure 2.1 Figure 2.2
Figure 2.3
a. What is the Thevenin equivalent resistance with respect to points a and b for each of the circuits:
Figure 2.1 (1 mark)
Figure 2.2 (1 mark)
Figure 2.3 (1 mark)
b. What is the Thevenin equivalent voltage Vab for the circuit in
Figure 2.1 (2 marks)
Figure 2.2 (2 marks)
Figure 2.3 (2 marks)
c. What is the maximum amount of power that can be dissipated in a load resistor placed between a and b in the circuit shown in Figure 2.1?
(2 marks)
3.. Consider the circuit shown in Figure 3.1 with unknown components X and Y. It is known that one of these is an ideal battery while the other one is a resistor. The voltage polarities across the resistors R2 and R5 are given as indicated in the diagram.
Figure 3.1
If the current through the resistor R2 is 0.25 A and the voltage across the resistor R5 is 2 V, what are each of the unknown components and what are their values?
Component X: Type : (1 mark)
Value : (1 mark)
Component Y: Type : (1 mark)
Value : (1 mark)
What is the voltage across R2? (1 mark)
What is the current through R5? (1 mark)
What is the current through the component X? (1 mark)
What is the voltage across the 8-W resistor? (1 mark)
How much power is delivered to the 1-W resistor? (1 mark)
4. Two circuit diagrams for simple analog meters (constructed with two identical meter movements) are shown in Figures 4.1 and 4.2.
Figure 4.1 Figure4.2
The voltmeter has been designed to measure a maximum of 12 V while the ammeter was designed to measure a maximum of 500 mA. The full-scale deflection current associated with the meter movement is 1 mA.
a. What is the total internal resistance of the voltmeter? (2 marks)
b. What is the shunt resistance of the ammeter, Rshunt? (2 marks)
c. The above voltmeter is connected to the circuits shown in Figures 4.3 and 4.4 with the correct polarity to measure the voltage between points a and b, what does it read?
Figure 4.3 V : (2 marks)
Figure 4.4 V : (2 marks)
d. How much work is needed to move a test charge of -1 C from point b to point a in the circuits shown in Figures 4.3 and 4.4 below?
Figure 4.3 Work: (1 mark)
Figure 4.4 Work: (1 mark)
Figure 4.3 Figure 4.4
5. For the RL circuit shown in Figure 5:
Figure 5
a. The switch is closed at t = 0, what is the time constant, t1, of the circuit? Hint: you must first find the Thevenin equivalent resistance seen by the inductor with the switch closed.
(1 mark)
b. Find the mathematical expressions for iL and vL during the storage phase.
iL= (1 mark)
vL= (1 mark)
c. The switch is reopened after five time constants have elapsed (t = 5t1). Find the new time constant, t2, of the circuit after the switch is opened. (1 mark)
d. Find the mathematical expressions for iL and vL during the decay phase.
iL= (1 mark)
vL= (1 mark)
e. What is the current through the inductor at t = 0.6 μs? (2 marks)
f. What is it that is being stored in the inductor? (1 mark)
g. Sketch iL and vL for 0 < t < 5t1+5t2. (1 mark each)
6 A simple magnetic circuit is shown below in Figure 6. It consists of a 100 turn coil wound around an iron core having a relative permeability of mr = 1500 and a uniform cross-sectional area of 25 cm2, and a 0.5 cm air gap. The mean length of the flux paths are also indicated on Figure 6. A magnetic flux of 2.5 μWb flows across the air gap.
a. What is the magnetic flux density in the air gap? (2 marks)
b. What is the magnetic flux density in the steel core? (2 marks)
c. What is the reluctance of the air gap? (2 marks)
d. What is the reluctance of the steel core? (2 marks)
e. What current is required to establish this flux? (2 marks)
Figure 6
7. The circuit shown in Figure 7 is in steady-state:
Figure 7
- Find the current through each of the following elements: (2 marks)
current through the 50 mH inductor
current through the 20 mH inductor
current through the 50 pF capacitor
current through the 120 pF capacitor
- Find the voltage drop across each of the following circuit elements: (2 marks)
voltage across the 50 mH inductor
voltage across the 20 mH inductor
voltage across the 50 pF capacitor
voltage across the 120 pF capacitor
- Find the energy stored in the 20 mH inductor. (2 marks)
- Find the energy stored in the 50 pF capacitor. (2 marks)
8. For the RC circuit shown in Figure 8.1 the switch is closed at t = 0. Initially (at the instant just before the switch is closed) the 3 mF capacitor has 12 mC of charge on it and the 2 mF capacitor is charged to 2 V.
Figure 8.1
- Find the initial charge on each capacitor and the initial voltage across each capacitor. (2 marks)
Capacitor / Charge on Capacitor / Voltage Across Capacitor
C1 = 3 µF / Q1 = 12 µC / V1
C2 = 2 µF / Q2 / V2 = 2 V
C3 = 4 µF / Q3 / V3
- Find the equivalent capacitance between the points a and b.
(2 marks)
- What is the initial voltage across the equivalent capacitor i.e. the voltage just before the switch is closed?
(2 marks)
- For the purpose of transient analysis reduce the circuit in Figure 8.1 with the switch closed to the equivalent circuit shown in Figure 8.2. (2 marks)
ETH =
RTH =
Figure 8.2
- What is the time constant of this circuit? (2 marks)
- At what time will the voltage across the equivalent capacitor equal 7.5 V?
(2 marks)
EP 155 Final Exam 2002 page 11 of 11