dec 2007
McGill University
FINAL EXAMINATION
Faculty of Engineering
FAMILY NAME (PRINT)
Fall 2007
FIRST NAME SECTION STUDENT I.D. (PRINT)
Circuit Analysis ECSE 210 Examiner: Prof. M. D. Levine
Co-Examiner: Prof. R. Khazaka
Signature:
Signature:
Date : Monday, Decmber 12, 2007
Time : 2:00 PM
INSTRUCTIONS • • • • • • • •
Explain clearly the steps in your solution. Use either a pen or HB pencil. The total number of points in this examination is 35, which will be pro-rated to 70% of the final grade. This is a closed book examination. Solutions to questions on the exam should be recorded in the provided exam booklets. You are permitted regular and translation dictionaries. Faculty standard calculator permitted only. This examination paper does not need to be returned.
E VALUATION OF EXAM PAPER
Question # 1 weight 6 score
2 4
3 8
4 7
5 5
6 5
Total Score
ECSE 210
1/3
December 12, 2007
[6 marks] 1. Consider the circuit below having a voltage v(t) across a 2H load: a. Find the Thevenin equivalent of the circuit to the left of the terminals a and b. [2 marks] b. Determine v(t). [2 marks] c. Determine the values of the circuit components for the Thevenin equivalent circuit found in (a). [2 marks]
[4 marks] 2. Consider the distribution of power from a source to a load. Suppose that the magnitude of the load voltage is 170 V, the transmission line resistance is 0.1Ω, and the load consumes 10kW of average power. Determine the line losses for a load power factor of 0.7 lagging. [2 marks] (b) Place a capacitor C across the load. Determine the value of C to correct the power factor of the parallel combination of the capacitor and the original load to unity, if the power frequency is 60 Hz. [2 marks] [8 marks] 3. (a) Determine the transfer function between. Vout and Vin for the circuit shown below. [2 marks] (b) Sketch the Bode magnitude plot and briefly explain in point form how you accomplished this. [3 marks] (c) Sketch the Bode phase plot and briefly explain in point form how you accomplished this. [3 marks]
ECSE 210
2/3
December 12, 2007
[7 marks] 4. (a)Find vc(t) after t=0 in the circuit shown below. [4 marks] (b) Sketch the pole-zero plot for this circuit. [1 mark] (c) Determine the time at which the response vc(t) is a maximum. [1 mark] (c) In one sentence, define the term “settling time”. [1 mark]
[5 marks] 5. (a) A balanced three-phase system with a line voltage of 300 V rms supplies a balanced Y-connected load with 1200 watts at a leading power factor of 0.8. Find the magnitude of the line current and the perphase load impedance. [3 marks] (b) A balanced 600-watt resistive load is added in parallel to the existing load in (a). If we assume that the phase voltage at the source is at 0o, determine the new line current. [2 marks] [5 marks] 6. A series RLC resonant circuit is connected to an input sinusoidal voltage source and the output is taken as the current in the loop. (a) Determine the expressions for the Q-factor and ωo. [3 marks] (b)What is the magnitude in dB and phase in degrees of the impedance at resonance if R=1Ω, L=1H and C=1F? [2 marks]
ECSE 210
3/3
December 12, 2007
FINAL EXAMINATION
Faculty of Engineering
FAMILY NAME (PRINT)
Fall 2007
FIRST NAME SECTION STUDENT I.D. (PRINT)
Circuit Analysis ECSE 210 Examiner: Prof. M. D. Levine
Co-Examiner: Prof. R. Khazaka
Signature:
Signature:
Date : Monday, Decmber 12, 2007
Time : 2:00 PM
INSTRUCTIONS • • • • • • • •
Explain clearly the steps in your solution. Use either a pen or HB pencil. The total number of points in this examination is 35, which will be pro-rated to 70% of the final grade. This is a closed book examination. Solutions to questions on the exam should be recorded in the provided exam booklets. You are permitted regular and translation dictionaries. Faculty standard calculator permitted only. This examination paper does not need to be returned.
E VALUATION OF EXAM PAPER
Question # 1 weight 6 score
2 4
3 8
4 7
5 5
6 5
Total Score
ECSE 210
1/3
December 12, 2007
[6 marks] 1. Consider the circuit below having a voltage v(t) across a 2H load: a. Find the Thevenin equivalent of the circuit to the left of the terminals a and b. [2 marks] b. Determine v(t). [2 marks] c. Determine the values of the circuit components for the Thevenin equivalent circuit found in (a). [2 marks]
[4 marks] 2. Consider the distribution of power from a source to a load. Suppose that the magnitude of the load voltage is 170 V, the transmission line resistance is 0.1Ω, and the load consumes 10kW of average power. Determine the line losses for a load power factor of 0.7 lagging. [2 marks] (b) Place a capacitor C across the load. Determine the value of C to correct the power factor of the parallel combination of the capacitor and the original load to unity, if the power frequency is 60 Hz. [2 marks] [8 marks] 3. (a) Determine the transfer function between. Vout and Vin for the circuit shown below. [2 marks] (b) Sketch the Bode magnitude plot and briefly explain in point form how you accomplished this. [3 marks] (c) Sketch the Bode phase plot and briefly explain in point form how you accomplished this. [3 marks]
ECSE 210
2/3
December 12, 2007
[7 marks] 4. (a)Find vc(t) after t=0 in the circuit shown below. [4 marks] (b) Sketch the pole-zero plot for this circuit. [1 mark] (c) Determine the time at which the response vc(t) is a maximum. [1 mark] (c) In one sentence, define the term “settling time”. [1 mark]
[5 marks] 5. (a) A balanced three-phase system with a line voltage of 300 V rms supplies a balanced Y-connected load with 1200 watts at a leading power factor of 0.8. Find the magnitude of the line current and the perphase load impedance. [3 marks] (b) A balanced 600-watt resistive load is added in parallel to the existing load in (a). If we assume that the phase voltage at the source is at 0o, determine the new line current. [2 marks] [5 marks] 6. A series RLC resonant circuit is connected to an input sinusoidal voltage source and the output is taken as the current in the loop. (a) Determine the expressions for the Q-factor and ωo. [3 marks] (b)What is the magnitude in dB and phase in degrees of the impedance at resonance if R=1Ω, L=1H and C=1F? [2 marks]
ECSE 210
3/3
December 12, 2007
