WLJT OLLEGES OF PPLIED SIENES In academic partnership with IRL INSTITUTE OF TEHNOLOGY Question ank ourse: E Session: 20052006 Semester: II Subject: E2001 asic Electrical Engineering 1. For the resistive circuit of Fig.(1), using the method of seriesparallel combination, find V 1 and I 2. nswers (V 1 = volt, I 2 = ampere). V 1 2 2. I 2 10V 50Ω 2 Fig.(1) 2. For the resistive circuit of Fig.(2), using the method of seriesparallel combination, find V 1 and I 2. nswers (V 1 = volt, I 2 = ampere). V 1 10V 2 2. 50Ω I 2 2 Fig.(2) 3. In the circuit of Fig.(3) each resistance is 1Ω. Find the value of V. 13V V Fig.(3) Prepared by Mohammad Mohatram 1
4. In Fig.(4) find the value of R eq 7Ω 3Ω Ω 4 N 2 R eq Fig.(4) Fig.(5) 5. For the circuit shown in Fig.(5), find the equivalent resistance between (i) and and (ii) and N 6. For the circuit of Fig.(6), find Nodal Voltages and urrent through the 2 Ω resistance. 7 12V Fig.(6) 7. In the circuit of Fig.(7) find the voltage V across the 6 Ω resistance using (i) nodal method and (ii) mesh method of circuit analysis. 8Ω 16V 30V V 1 Fig.(7) Prepared by Mohammad Mohatram 2
8. For the circuit of Fig.(8), find Nodal Voltages. From the symmetry of Nodal Equations attempt to draw generalized conclusions. 1 2 2 4 3 4 5 3 6 Fig.(8) 9. In the bridge circuit of Fig.(9), find the current through resistance connected between D. It is suggested that you use Mesh method of analysis. 100Ω 100Ω 1Ω 5 I 150Ω 20Ω D 200Ω 5V 3Ω 12V Fig.(9) Fig.(10) 10. For the circuit of Fig.(10), determine the current in all the elements. 11. Using nodal techniques, determine I 1 in the circuit of Fig.(11). Prepared by Mohammad Mohatram 3
1 5 4I 1 4 Fig.(11) 12. For the circuit of Fig.(12), write the nodal equations in terms of node to datum voltages V 1 and V 2. Solve for V 1 and V 2. Hence find: i. direction and magnitude of current through 5 Ω resistance. ii. power output and input to the current and voltage sources Hint: (Voltage source being ideal can not be converted to current source) V 1 V 2 1 5V Fig.(12) 13. Using Mesh analysis find currents I 1, I 2 and I 3 in the circuit of Fig.(13). lso find the power supplied by the two current sources. 20Ω 40Ω I 1 I 2 0.5 60Ω 1 100Ω 0.6 I 3 10V Fig.(13) 14. Find the voltage across resistance in Fig.(14) using (i) nodal analysis and (b) mesh analysis. Prepared by Mohammad Mohatram 4
20Ω 12V 12V 20I 1 Fig.(14) I 1 40V 15. The circuit of Fig.(15) represents a transistor amplifier. Find (i) I 2 /I 1 and (ii) Ratio of power consumed by 5 kω resistance to the power supplied by 0.5V source. 500Ω 0.5V I 2 I 1 1kΩ 50kΩ 0.3V 1 Fig.(15) 16. a) State and explain KL and KVL. b) State and prove maximum power transfer theorem for D networks. c) State and explain superposition theorem. d) State and explain Thevenin's theorem. e) State and explain Norton's theorem. 17. In the circuit of Fig.(16) find a) I s when I = 0 and V s = 16 volts. b) V s when I = 0 and I s = 16 amperes. V s I I s Fig.(16) Prepared by Mohammad Mohatram 5
18. For the circuit of Fig.(17) find V and I by using the principle of superposition. 0.1Ω 0. 0.1Ω 60V V I 10V Fig.(17) 19. For the circuit shown in Fig.(18) find the Galvanometer (G) current using Thevenin equivalent as seen at terminal pair D. 1 G V 2 V 1 1 D 1 16V 0.5V 2 8Ω I 10 V Fig.(18) Fig.(19) 20. In the circuit of Fig.(19) find the value of I to reduce the nodedatum voltage V 1 to zero. 21. For the circuit of Fig.(20) find Thevenin equivalent as viewed by the resistance R. Find the value of resistance R for maximum power dissipation in it and the value of this power. R Ω 11/8Ω 30Ω 1Ω 3Ω 4V 1 1 2 11V x y Fig.(20) Fig.(21) 22. Find the Thevenin equivalent of the circuit shown in Fig.(21) as seen at terminal pair xy. Prepared by Mohammad Mohatram 6
23. In the circuit of Fig.(22) find the current I using the principle of superposition. 1. 1Ω 6V I 1 I 2 3Ω I 3 4 Fig.(22) 24. Find the Thevenin equivalent of the circuit of Fig.(23) to the left of xy. 9 1Ω 9V 3Ω Fig.(23) x y E 0.01Ω 30 F 0.0 80 0.0 60 70 0.01Ω 0.01Ω 120 D 0.03Ω 60 Fig.(24) 24. Find the current in all the branches of the network shown in Fig.(24). 25. Find the value of R and the current flowing through it in the accompanying network Fig.(25) when the current is zero in the branch O. X O R Ω 10 3Ω 8Ω 1 V Prepared by Mohammad Mohatram 7
Fig. (25) Fig.(26) 26. Use the network reduction (stardelta) to determine the voltage V in the network of Fig.(26). 27. Use the Nodal analysis to find the voltage across 1 resistance in the circuit of Fig.(27) and verify your answer by Thevenin's and Norton's theorem. 3Ω V 1 13V V 1 /3 1 Fig.(27) 28. Use the Mesh analysis to determine the currents I 1, I 2, and I 3 in the circuit of Fig.(28) and verify your result by nodevoltage analysis. 20Ω 40Ω 0.6 V 50Ω I 1 V 6V I 3 I 2 0.4 V c 120Ω Fig.(28) 29. Use the Mesh analysis to determine the voltage across 12 Ω resistance in the circuit of Fig.(29). Verify the result by using: a. Nodal analysis b. Thevenin's theorem c. Norton's theorem d. KVLKL Prepared by Mohammad Mohatram 8
12 1/ 1/ 1/8Ω 48 3Ω 8Ω 1 V 4V 1/ 8 4V Fig.(29) Fig.(30) 30. Find the voltage across 8 current source in the circuit of Fig.(30) by the Nodevoltage method. (Hint: The 4 V source has no series resistance and can not be converted into a current source equivalent. Select node D as the reference and write the node voltage equations in the usual manner. Then, recognition that V c is known leads to the desired solution). 31. Verify the answer in Q.(30) by a. Thevenin's theorem b. Norton's theorem c. Mesh analysis d. KVLKL 31. Find the power supplied by the 9 source in the circuit of Fig.(31) by using Mesh analysis. 9 12V Fig.(31) 20Ω 2 1 b 1 2 a 1 1 1 Fig.(32) 1 2 32. network of 9 conductors connect 6 points,,, a, b, and c as shown in Fig.(32). The figure denotes resistance in ohms. Find: i. the resistance between and a; ii. the resistance between and a; iii. the resistance between c and a; iv. the resistance between and 33. Use the principle of super position to find the value of I needed to cause V 2 = 0 in the circuit of Fig.(34). Prepared by Mohammad Mohatram 9
10V 20 I 1 2I 1 V 2 I Fig.(34) 35. In the circuit of Fig.(35), what resistor R L connected across terminals a and b will absorb maximum power and what is this power? a 10I 8 40Ω R L b Fig.(35) 36. Determine the Thevenin equivalent circuit as viewed by the resistor R in the circuit of Fig.(36) b. What value of R is required if the power dissipated by R is to be maximum? c. What is the value of the power in b? d. lso find out efficiency of power transferred to R under the condition of maximum power transfer. a R Ω 20Ω b 3 1 4V Fig.(36) 26. a. Obtain Thevenin equivalent circuit at terminals for the circuit of Fig.(37). ns. V o = 0.257V. Prepared by Mohammad Mohatram 10
b. What is the maximum power that can be provided to a resistance R connected to terminals? ns. 2.03 mw 40Ω 1 0.55V 30Ω 3V Fig.(37) 27. Explain with the aid of a sketch how the R.M.S. value of an alternating current is obtained. n alternating current is represented by i=10 sin 942t amperes. Determine: (a) the frequency; (b) the period; (c) the time taken from t = 0 for the current to reach a value of 6 for a first and second time; (d) the energy dissipated when the current flows through a 20 resistance for 30 minutes. nswers: (a) 150Hz (b) 6.67ns (c) 0.68ms (d) 0.5 kwh 28. Define and explain RMS and verage value. 29. Explain the significance of the root mean square value of an alternating current or voltage waveform. Define the form factor or such a waveform. alculate from first principles the r.m.s. value and form factor of an alternating voltage having the following values over half a cycle, both half cycles being symmetrical about the zero axis: Time in milliseconds: 0 1 2 3 4 Voltage in volts: 0 100 100 100 0 These values are joined by straight lines. nswers: (81.5 V; 1.087) 40. constant current of 5 flows for 0.04 second, and to complete the cycle, a constant current of 2 flows in the opposite direction for 0.06 second. Sketch the waveform of the current over one cycle and calculate: (a) the mean value of the current. (b) the r.m.s. value of the current. (0.8; 3.52 ) 41. Find the resultant of the following two alternating voltages : π V1 = 150sin ωt 3 π V2 = 250sin ωt 4 ns. V = 397sin(ωt 50.7 0 ) 42. Two voltages given by V 1 = 50 sin(ωt 30 0 ) and V 2 = 20 sin(ωt 45 0 ) act in the series circuit. Determine: (a) the frequency of the total voltage; (b) r.m.s. value of the total; voltage. Draw the phase or diagram. (60Hz; 41 8 V) Prepared by Mohammad Mohatram 11
43. In a parallel circuit with three branches, the instantaneous branch currents are represented by I 1 = 10 sing (θ 45 ) I 2 = 5 cosθ I 3 = 5 sin (θ 30 ) alculate the total instantaneous current and express the results in the same form. I = 11.5 sin (θ 7 ) 44. Two wires carrying currents i 1 and i2 join a third wire and this the carried the sum of these two currents. i 1 = 10 Sin wt & i 2 = 15 sin ( wt 45 ) cos 3 wt. What will be the equation of the current in the third wire? What will be reading of an ammeter when connected in each of the lines with the above currents following. 45. Determine power delivered to a 50 Ω resistor by each of these (i) 1 sin 2000t 2 cos 5000t volts, (ii) 10 sin 2000t 2 cos 2000 t volts, (iii) 10 sin 2000t 2 sin 2000 t volts. 46. (a) Determine the reading of an voltmeter across whose terminals is applied a voltage wave e = (200 sin wt 50 sin 3t) volts (b) What would be the reading of a D voltmeter in this voltage wave? 47. n iron cored coil takes 4 at a power factor of 0.5 when connected to a 200V;50Hz supply, When the iron core is removed and the voltage is reduced to 40 V the current rises to 5 at a power factor of 0.8. Find the iron loss in the core and the inductance in each case. 48. n inductive coil takes 10 and dissipates 1000W when connected to a supply at 250V;50Hz. alculated (a) the impedance (b) the effective resistance (c)the reactance (d) the inductance (e) the power factor (f) the angle of lag. { (a) 25 (b) 10 (c) 22.0 (d) 0.146 H (e)0.4 (f) 66.4 }. 49. n iron cored coil of resistance 5 Ω taken 10 when connected to 200V;50Hz mains, and the power dissipated is 750W. ssuming the coil to be equivalent to a series impedance, calculate (a) the ironloss (b) The inductance at the given value of the current (c) the power factor. {(a) 250W, (b) 0.059H, (c) 0.375}. 50. When a resistance and an inductor in series are connected to a 240V supply, a current of 3 flows lagging 37 behind the supply voltage, while the voltage across the inductor is 171V. Find the resistance of the resistor, and resistance and reactance of the inductor. { 33.26; 30.74; 48 Ω) 51. Find an expression for the current, and calculate the power, when a voltage represented by V = 283 sin 100πT is applied to a coil having R= 50 Ω and L=0.159H. { 4 sin ( 100π t π /4, 400 W}. 52. voltage of 200V is applied to a series circuit consisting of a resistor, an inductor and a capacitor. The respective voltage across these component are 170, 150 and 100V and the current is 4. Find the power factor of the inductor of the circuit. {0.16; 0.97} 53. 230V, 50Hz voltage is applied to of coil L=5H and R=2 Ω in series with a capacitance. What value must have in order that the p.d. across the coil shall be 250V? {26 angle F} 54. Draw a vector diagram for the circuit shown in Fig.(38) indicating the terminal voltage V 1 and V 2 and the current. Find the value of (a) current (b) V 1 and V 2 (c) the power factor. {(a) 5.84, (b) 108.2V, 221.5V (c) 0.875 leading} Prepared by Mohammad Mohatram 12
0.05H 20Ω 0.1H 50µF V 1 V 2 V = 240 volt, 50 Hz Fig.(38) 55. In the arrangement shown in Fig.(39), has a capacitance of 20 µf, and the current flowing through the circuit is 0.345. If the voltages are as indicated, find the applied voltage, the frequency, and the loss in the ironcored inductor L. R L 25 V 40 V 55 V 50V Fig.(39) 56. For the circuit shown in Fig.(40),Find the values of R and so that V b = 3V a and V a & V b are in Quadrature. Find also the phase relation between V and V b. 0.0255H R V b V a V = 240 volt, 50 Hz Fig.(40) Prepared by Mohammad Mohatram 13
57. Two impedances, Z 1 and Z 1 are connected in parallel. The first branch takes a leading current of 16 and has a resistance of while the second branch takes a lagging current at power factor 0.8. The total power supplied is 5KW, the applied voltage being 100j200V. Determine the complex expressions for the branch and total current, and for the circuit constants. I 1 = 10.8 j 11.8; I 2 = 18.7 j 9.3; I = 7.9 j 21.1 Z 1 = 5.0 j 13.1; Z 2 = 8.75 j 6.42; Z = 9.85 j 1.05 58. circuit, with two branches Y 1 = 0.16 j 0.12 Ω and Y 2 = j0.15 Ω in parallel, is connected to a 100V supply. Find the total loss and and the phase relationship between the branch currents and the supply current. (1600W, I 1 leads by 47.5, I 2 lags by 79.5 ) 59. sinusoidal, 50Hz voltage of 200V supplies the three parallel circuits shown as shown in Fig.(40). Find the current in each circuit and the total current. Draw the vector diagram. 3Ω 0.03H 1 100Ω 400µF 2 7Ω 0.02H 300µF 3 Fig.(41) (2) 2 (3) 24.3 (4) Total 29.4} {(1) 20.2 60. voltage of 240V is appklied to a pure resistor, a pure capacitor and an inductor, all in parallel. The resultant current is 2.3. While the component current are 1.5, 2.0 and 1.1 respectively. Find the resultant power factopr and the power factor of the inductor. [ 0.88, 0.5] 61. Find what inductance must be placed in series with a lamp requiring 3.05, 410W at unity power factor, when the supply is 230V, 50Hz. Find also the value of capacitance which must be placed across the power terminals to raise supply power factor to unity. [0.19H; 34.1µF] 62. coil having a resistance of and an inductance of 1H is connected in parallel with a circuit comprising a similar coil in series with a capacitor and a noninductive resistor R. alculate the values of and R so that the current in either branch of the arrangement are but differ in phase by 90. Frequency 50Hz. Prepared by Mohammad Mohatram 14
[=10.3µF R=3] 63. reactor has a resistance of 5 Ω and an inductance of 0.04 H. Find a suitable shunt circuit such that current taken by the combination will be 20 at 100V, at all frequencies. [5 Ω; 1600µF] 64. voltage of 100V is applied across to produce I = 40. Find the value of R when (a) Rp = 5 Ω ; (b) 10 Ω ; also the power factor of the circuit in each case. [(a) 1.12 Ω, 0.725 Ω; (b) 1.22 Ω, 0.642] X p = R p Fig.(41) 65. capacitor of 50µ, shunted by a noninductoive resistor of 100 Ω, is connected in series with a resistor of 50 Ω to a 200V,50Hz supply. alculate (a) the current in the capacitor; (b) the current in the chunted resistor; (c) the total current. [(a) 1.85, (b) 1.18, (c) 2.20] 66. In the circuit shown determine what 50Hz voltage mist be applied across in order that a current of 10 may flow in the capacitor. [ns. 288V] 0.0191H 3Ω 0.0318H 7Ω 398µF Fig.(42) Prepared by Mohammad Mohatram 15
67. 100 Ω resistor, shunted by a 0.4H inductor, is in series with a capacitor. voltage of 250V at 50Hz is applied to the circuit. Find (a) the value of to give unity power factor, (b) the total current, and (c) the current in the inductive branch. Draw the vector diagram. [64.9µF, 4.07, 2.54] 68. The circuit shown takes 12 at a lagging power factor and dissipates 1.8 kw when the voltmeter reading is 200V. alculate the value of R 1, X 1 and X 2. [ R 1 = 3.14; X 1 = 2.17; X 2 = 13/32] R 1 X 1 X 2 20Ω 200V V Fig.(42) 69. n inductive impedance is connected in series with a parallel combination consisting of a capacitor and a noninductive resistance. The circuit constants are so adjusted that the current in the parallel branches are equal, and that the voltage across is equal to and in quadrature with voltage across. When a voltage of 200V is applied to, the total power absorbed is 1200W. alculate the circuit constant and draw a vector diagram. [R = X = 16.6; R = X = 33.3 Ω] 1Ω 0. 0.8H 0. 1Ω 100V Fig.(43) Prepared by Mohammad Mohatram 16
70. Determine the impedance of the circuit shown and the power consumed in each branch. [ 1.12 29.5 Ω, 0.216kw, 1.24kw, 3.10kw, 3.16kw] 71. sigle phase load of 5kw operates at a power factor of 0.6 lagging. It is proposed to improve the power factor to 0.95 lagging by connecting a capacitor across the load. alculate the kvar rating of the capacitor. [5.0232KVR] 72. 3.73kw, 1 phase, 200V motor runs at an efficiency of 75% with a p.f. of 0.7 lagging. Find (i) the real input power (ii) the kv taken, (iii) the reactive power and (iv) the current. With the aid of a vector diagram, calculate the capacitance required in parallel with the to improve the p.f. to 0.9 lagging. The frequency is 50Hz. [4.97kw; 7.1kV, 5.07KVR, 35.5; 212 µf] 73. voltage of 200< 30 V is applied to two circuits and connected in parallel. The current in is 20<60 and that in 40/30. Find the kv and kw in each brabch circuit, and the main circuit. Express the current in the main circuit in the form a j. [ kv=4; kv=8; kv 12; kw = 3,46; kw = 4; kw =n 7.46; I = 44.64j2.68] 74. n inductive coil having a resistance of 1 takes a current of 4 Prepared by Mohammad Mohatram 17