EL162_CIRCUIT_THEORY_2019_1.pdf

UNIVERSITY OF MINES AND TECHNOLOGY, TARKWA SECOND SEMESTER EXAMINATIONS, APRIL/MAY 2019 COURSE NO : CE, EL 162 COURSE NAME: CIRCUIT THEORY CLASS:...

UNIVERSITY OF MINES AND TECHNOLOGY, TARKWA SECOND SEMESTER EXAMINATIONS, APRIL/MAY 2019 COURSE NO : CE, EL 162 COURSE NAME: CIRCUIT THEORY CLASS: CE/EL I TIME: 3 HOURS Name: __________________________________________ Index Number: _______________ SECTION A Attempt all questions in this section. For each question, write the letter corresponding to the correct answer in your answer sheet provided. The switches in the circuit shown in Figure 1 are initially closed for a long time before opening simultaneously at t = 0. Figure 1 Circuit Diagram for Questions 1 and 2 Using the above information, determine the correctness or otherwise of the following Assertions [A] and the Reasons [R] provided. 1. Assertion [A]: The voltage across the capacitor just before the switches operate (t = 0-) is the same as just after they operate (t = 0+). Reason [R]: Current through a capacitor cannot change instantaneously. A. Both [A] and [R] are true and [R] is the correct reason for [A] B. Both [A] and [R] are true but [R] is not the correct reason for [A] C. [A] is true but [R] is false D. Both [A] and [R] are false 2. Assertion [A]: A long time after the switches operate (t = +∞) the voltage across the capacitor will be zero Reason [R]: Voltage across a capacitor cannot change instantaneously. A. Both [A] and [R] are true and [R] is the correct reason for [A] B. Both [A] and [R] are true but [R] is not the correct reason for [A] C. [A] is true but [R] is false D. Both [A] and [R] are false The switch in the circuit shown in Figure 2 has been in position a for a long time. At t = 0 the switch moves to position b. Use this information to answer Questions 3 to 5. Page 1 of 8 3. Find the initial voltage drop across the capacitor vc(0) at time t ≤ 0 A. 20 V B. 15 V C. 12 V D. 0 V 4. Determine the final voltage on the capacitor vc(∞) at t = ∞ A. 0 V B. 20 V C. 40 V D. 50 V 5. The time constant τ of the circuit will be A. 1 ms B. 2 ms C. 3 ms D. 4 ms Figure 2 Circuit Diagram for Questions 3 through 5 6. For the circuit shown in Figure 3 (a), find the Norton’s equivalent impedance ZN external to the terminals a and b. A. ZN = 18.11 Ω6o C. ZN = 4.55 Ω 8o B. ZN = 10.00 Ω 0o D. ZN = 5.00 Ω 0o Figure 3 Circuit for (a) Questions 6 and 7 (b) Question 8 7. For the circuit shown in Figure 3 (a), find the Norton’s equivalent current IN external to the terminals a and b. A. IN = 2.00 A0o C. IN = 12.50 A0o B. IN = 4.80 A24o D. IN = 16.00 A42o 8. For the circuit of Figure 3 (b), determine the Laplace transform representation of the current i1(s) when is close at t = 0 [Assume initial current in the inductor is 0]. 4 3 A. I1 ( s)  C. I1 ( s)   s  2  s  3  s  2  s  2  4 3 B. I1 ( s)  D. I1 ( s)   s  2  s  3  s  2  s  4  Page 2 of 8 9. The admittance Y of an impedance given as Z = 2 + j 4 , A. Y = 2.0 + j 4.0 S C. Y = 0.1 - j 0.2 S B. Y = 0.5 + j 0.25 S D. 2 + j 0.25 S 10. A 4  resistor is connected in series with an 8 mH inductor. At what frequency does the phase angle of the combined impedance equal 56.45o. A. 120 Hz B. 100 Hz C. 60 Hz D. 50 Hz 5 11. V is equivalent to 2  j2 A. 1.77 V -45o C. 0.71 V 45o B. 0.45 V90o D. 2.33 V 90o 12. Find the total impedance of a circuit consisting of a 40 Ω resistor connected in series with a 50 mH inductor and a source at 0 Hz. A. 90 Ω B. 40 Ω C. 50 Ω D. 0 Ω 13. Source transformation allows a current source in ___ with an impedance to be converted into a voltage source in ___ with the same impedance A. Series, Parallel C. Series, Series B. Parallel, Series D. Parallel, Parallel 14. The impedance of a capacitor connected across a DC source is effectively ____ A. Zero C. Sinusoidal B. Infinite D. Exponential 15. A voltage controlled current source gives out constant ________ whose value is determined by _____ elsewhere. A. Current, current C. Voltage, current B. Voltage, voltage D. Current, voltage The switch in the circuit shown in Figure 4 has been open for a long time. At t = 0 the switch is closed. Use this information to answer Questions 16 to 18. 16. The initial current flowing through the inductor will be A. 2 A B. 3 A C. 5 A D. 12.5 A 17. The current of the inductor at t = ∞ is A. 0 A B. 2 A C. 5 A D. 12.5 A 18. The expression for the current at all time t ≥ 0 is A. i (t )  2  3e 40t C. i(t )  5  3e250t B. i (t )  12.5  7.5e40t D. i(t )  5  7.5e250t Page 3 of 8  Figure 4 Circuit Diagram for Questions 16 to 18 19. The Fourier ttransform of the impedance of an 80 mH inductor connected across a 50 Hz source is A. j25.15 Ω B. j4.0 Ω C. -j50.0 Ω D. 64.3 Ω 20. A current is given as  j 20e j 30 A, this current can equally be expressed as o A. 20e j 30 o o C. 20e j 60 B. 20e  j120 D. 50e o o j 60 21. Source transformation of the voltage source of Figure 5 (a) yields a current source ______ in parallel with Z. A. I = 0.3125 mA∠ -60o C. I = 80 mA∠ -60o B. I = 0.3125 mA∠ 60o D. I = 3.2 mA∠ 30o Figure 5 Circuit for (a) Question 21 and (b) Question 22 22. Determine in Ohms, the equivalent impedance Zeq of the circuit in Figure 5 (b) A. 65 B. 50 – j30 C. 50 + j30 D. j65 23. The current I= 20 A30o is equivalent to A. 17.32 + j10 V C. 35 V B. 20+ j15 V D. 5 V 8 24. A circuit has a transfer function H ( ) . Its inverse Fourier transform is 1  j 4 A. 8e t 1  t 2 C. 2e. B. 8e0.25t 0.25t D. 2e 25. An alternating sinusoidal current has RMS value of 20 mA and a frequency of 50 Hz. This current can be expressed as Page 4 of 8  A. 20sin50t mA C. 50sin20t mA B. 28.28sin314.16t mA D. 28.28sin50t mA 26. As the supply frequency increases, the impedance of a capacitor _______ A. Decreases C. Fluctuates B. Increases D. Remains the same 27. A voltage controlled current source gives out constant ________ whose value is determined by _____ elsewhere. A. Current, current C. Voltage, current B. Voltage, voltage D. Current, voltage 28. The node voltage method is based on A. Kirchoff’s voltage law C. Ohm’s law B. Kirchoff’s current law D. Millman’s theorem 29. A resistor and an inductor are connected in series across a voltage source. As the frequency of the voltage source increases, the ____ increases while the _____ decreases A. Total impedance, Resistance of the resistor B. Total impedance, current C. Inductance of the inductor, Resistance of the resistor D. Inductance of the inductor, Total impedance 30. In a purely resistive circuit, current A. Lags behind the voltage by 90o C. Can lead or lag the voltage by 90o B. Leads the voltage by 90o D. Is in phase with the voltage 31. The AC voltage rating of an electrical appliance is 100 V. This number represents __ value A. Average B. RMS C. Peak D. Median 32. The capacitive reactance of a capacitor is given as 10 Ω. Its impedance in complex representation is A. 10 Ω B. –j 0.1 Ω C. –j10 Ω D. j10 Ω 33. Given I  j(5  j12) A , find the corresponding i(t) in sinusoidal form. A. i(t) = 13cos(ωt + 22.62o) A C. i(t) = 13cos(ωt + 67.38o) A B. i(t) = 13cos(ωt - 22.62o) A D. i(t) = 13cos(ωt - 67.38o) A 34. The complex number 1+ j is equivalent to A. 2e j 45 B. B. 2e j 0 C. 1e j 45 D. 1 35. Any branch of an electrical circuit has the same ___ along its length A. Voltage C. Resistance B. Current D. Admittance 36. When two or more circuit elements are connected in series A. the currents flowing through them are the same B. the voltages across them are the same C. the powers dissipated in them are the same Page 5 of 8  D. the energies stored in them are the same 37. Kirchhoff's Current Law (KCL) can be stated as A. The sum of the currents flowing into any node is zero B. The sum of the currents flowing around any closed loop is zero C. The sum of the currents through all elements equals the sum of the voltages across the elements D. The current through an element is proportional to the voltage across the element 38. The relationship between the phasor voltage V, the phasor current I and the impedance Z is A. I = Z V C. Z = V + I B. Z = V I* D. V = Z I 39. The impedance of a resistor R at angular frequency  is A. Z = j R C. Z = R B. Z = j  R D. Z = 1 / R 40. "In any network containing more than one source of e.m.f., the current in any branch is the algebraic sum of a number of individual currents, each of which is due to each source of e.m.f. acting alone when the remaining sources of e.m.f. are replaced by short circuts" The above statement is associated with A. Thevenin's theorem C. Superposition theorem B. Norton's theorem D. None of the above Page 6 of 8  SECTION B Attempt ONLY TWO questions in this section. Each question carries equal marks. Answer the questions in your answer booklet. PART I Methods of AC Circuit Analysis and Network Theorems Question 1 (20 marks) a) Find the Norton’s equivalent circuit for the network external to terminals a and b in Figure 6(a). [10 Marks] b) Use your solution in 1a) to determine the current flowing through the 10 Ω resistor. [3 Marks] c) Determine the voltage across the 5 kΩ resistor in figure 6 (b). [7 Marks] Figure 6 Circuit for (a) Problem 1a) and b); (b) Circuit for Problem 1 c) PART II First Order Circuits Question 2 (20 marks) The two switches shown in the circuit in Figure 7 operate simultaneously. Prior to t = 0 each switch has been in its indicated position for a long time. At t = 0 the two switches move instantaneously to their new positions. Find a) io(0), the initial current flowing through the inductor for t ≤ 0 [5 Marks] b) io( (t), the expression for the inductor’s current for t ≥ 0 [5 Marks] c) vR(2) (t) , the expression for voltage across the 20 kΩ resistor for t ≥ 0 [5 Marks] d) The value of the current through the inductor after 2 ms [5 Marks] Figure 7 Circuit Diagram for Question 2 Page 7 of 8  PART III Laplace Transform, Fourier Transform and Circuit Analysis [Tables of Laplace and Fourier Transforms will be provided on request] Question 3 (20 marks) The switch in the circuit shown in Figure 8 has been in position a for a long time. At t = 0, the switch moves to position b. a) Using the Laplace transform approach, write the expression for the capacitor’s voltage vo(t) for time t ≥ 0. [10 Marks] b) Using the solution in 3(a) above, determine the current io(t) flowing through the capacitor for any time t ≥ 0. [3 Marks] Figure 8 Circuit Diagram for Questions 3 (a) and (b) c) Using the Fourier transform, write the frequency domain expression for each of the loops indicated in Figure 13 given that is(t) = 4e-tu(t) V. [7 Marks] Figure 9 Circuit Diagram for Questions 3 (c) F. Mumuni/ Dr S. Nunoo Page 8 of 8