3. The current through a given section is steady at 30 pa. How long does a charge of 12 μc take to cross the section? (111 hours)

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1 UNIVERSITY OF TECHNOLOGY ELECROMECHNICAL DEPARTMANT SYSTEMS BRANCH Dr. Sameir Abd Alkhalik Aziez FIRST YEAR ELECTROMECHNICAL ENGINEERING BASICS ELECRICAL ENGINEERING Question Sheet (1) 1.Give the dimensions (units) for each of the fallowing quantities : - rate of flow of charge ; rate of loss of energy; rate of gain of energy; rate of doing work; energy loss per unit charge; energy gain per unit charge; work per unit charge. 2. Find, the current resulting from the "steady flow of (a) 90 C in 6 s; (b) 900 C in 20 minutes; and (c) 4x10 23 electrons in 5 hours. (15 A, 0.75 A, 3.56 A) 3. The current through a given section is steady at 30 pa. How long does a charge of 12 μc take to cross the section? (111 hours) 4. A light bulb draws a steady current of 0.5 A; what is the charge transported through the bulb in 1 minute? (30 C) 5. A 2000 Kg lift rises 50 m in 25 s; what is the average power? (39.2 KW) 6. Find the voltage between points a and b if 24 J are required to move, from a to b, a charge of (i) 3 C; (ii) -4 C; (iii) 20 x electrons. (8 V, a low; 6 V, a high; V, a high) 7. What is the current drawn by a 220 V, 60 W light bulb? What is the energy it consumes in 1 s? In 1 minute? In 1 hour? (272.7 ma; 60 J; 3.6 KJ; 216 KJ) - 1 -

2 8. A 6220 V, 60 W light bulbs is switched on for 5 hours every day. What is the monthly cost if the electrical rate is 0.01 ID/KWh (Iraqi dinare per kilo watt hour)? (0.09 ID = 90 fils ) 9. Find the voltage across a light bulb if a 0.5 A current flowing through it for 4 s causes the light bulb to give off 480 J of light and heat? (240 V) 10. Batteries are usually rated by their voltage and their Ampere hour: a 12 V, 45 Ah car battery can deliver 4.5 A for 10 hours, or 9A for 5 hours, or 15 A for 3 hours, etc. What is the energy stored in this battery? (1.9 MJ) 11. A small transistor radio works at 6 V, and draws a current of 20 m A. It is supplied by 4 batteries, each rated at 1.5 V, 80 mah. (i) How many joules can the batteries supply? (ii) what is the average power consumed by the radio? (iii) how long can the radio be operated? (1.728 KJ; 120 mw; 4 hours) 12. How long does it take a 100 W electric light to consume energy worth 5 ID if the electric rate is ID/KWh? How long does it take a 2 KW heater? (3333 hours = 140 days ; 167 hours = 7 days) 13. If the electric rate is 20 fils/kwh, how many joules does a dinar buy? (180 MJ) 14. A metal sphere is moved at a uniform speed a distance of 8 m. The sphere is charged with 250 μc, and its motion is opposed by a uniform force of 450 nn. Find the energy gained by the charge, and the potential difference between the initial & final points.( 3.6 μj ; 14.4 mv ) - 2 -

3 15. Complete the following table using suitable units :- resistance current voltage power 1? 4 A 12 V? 2 20 ohms 3.8 A?? ohms? 7.3 V? 4? 6.3 A 240 V? 5? 42 μa 8.4 V? M - ohms? 140 V? 7 22 K ohms? 180 V? 8 50 K ohms 2.1 ma?? M ohms? 17 KV? ohms 91.5 A?? 11? 31 KA 240 V? 12? 30 A? 72 KW 13? 500 A 75 mv? M ohms?? 2 W 15?? 220 V 75 W ( domestic lamp ) 16? 12 V 5 W ( car lamp ) 16. A 330 ohm resistor is rated at 0.5 W. What is the maximum allowable voltage? (12.85 V) 17. A 3.3 MΩ resistor is rated at 2.5 mw. What is the maximum allowable current? voltage? (27.5 μa; 90.8V) 18. A wire is 3 Km long and has a radius of 4.5 mm. The resistivity is 1.6 μωcm, Find the resistance of the wire. (755 mω ) - 3 -

4 19. A 100 m aluminum cable carries a current of 30 A at 20 C. It is required that the voltage drop along the wire does not exceed 6 V. What is the minimum allowable cross-sectional area of the wire? (14.15 mm 2 ) 20. A cable transports power from a generator to a factory 80 m away. The factory load is 200 A. The cable core has o resistivity of μωcm, and a diameter of 10 mm. Find the voltage drop in the cable. (7.0 V) 21.A coil consists of 200C turns of wire having cross sectional area 0.8 mm 2, and resistivity 0.02 μωm at the working temperature. The mean length per turn is 80 cm. calculate the power dissipated in the coil when it is connected to a 110 V dc supply. ( W ) 22. A coil of copper wire is 200 m long. A coil of aluminum wire has the same resistance and cross sectional area; what is its length? (121.6 m) 23. A two-wire distributor is 400 m long. It is fed from one end at 240 V. There is a load of 200 A at a distance of 250 m from the feeding end, and a load of 160 A at the far end. The total voltage drop must not exceed 4 %. The resistivity of the conductors is 2 micro-ohm-cm at the working temperature. Find the minimum allowable cross-sectional area of the wires? (475 mm 2 ) 24. If the distributor of question 23 works 24 hours a day every day of the year, find the yearly cost of the energy loss, assuming an electrical rate of 0.01 ID/K.Wh. How can this cost be decreased at the design stage? (267 ID) 25. A cylindrical iron rod is 66 cm long; its diameter is 3 mm. Find the resistance at a temperature of 72 o C. (1.654 milli-ohms) - 4 -

5 26. A coil of copper wire has a resistance of 38 ohms at 28 C. Find its resistance at 75 C & at -15 C. (44.8 ohms; 31,8 ohms) 27. The voltage drop across a 500 cm long copper conductor is 400 mv. The cross-sectional area is 2.5 mm 2, and the temperature is 65 o C. Find the power consumed in the conductor. (3,95 W ) 28. A 2.5 mm 2 cable is 500 m long. It is connected to a 200 V supply at one end, and short-circuited at the other end. The resistivity is 2.60 micro-ohm-cm at 0 o C, and 2.83 micro-ohm-cm at 20 o C. Find the short-circuit current if the coble temperature is 50 o C. (15.75 A) 29. The voltage and current in a copper conductor at 20 C are 240V and 4.8A respectively. Find the conductor temperature when it is consuming 900 W at the same voltage. (91.3 o C) 30. A wire is 120cm long; its cross-sectional area is 1.5 cm 2. The conductivity is 32*10 6 mho/m at 75 o C, and 40*l0 6 mho/m at 35 o C. Find the resistance of the wire at 50 C. (21.9 milli-ohms) 31.The resistance of a coil was found to be 36 milli-ohms at a temperature of 80 o C, and 29 milli-ohms at 15 o C. At what temperature will the resistance be 32 milli-ohms? (42.9 o C) 32. A conductor is 160 cm long; its cross-sectional area is 0.8 mm 2. The conductivity is 50*10 6 mho/m at 60 o C; the temperature coefficient of resistance is 3.4*l0-3 ( C) -1, also at 60 o C. Find the resistance at 85 C. (43.4 milli-ohms) - 5 -

6 33. Constantan wire of 0.2 mm diameter is wound around a plastic cylinder of 1.0 cm diameter to make a wire-wound resistor. How many turns are needed to obtain a resistance of 50 ohms if the resistivity is49 micro-ohm-cm? (102 turns) 34. A voltage of 1.5 V is applied to a 7.5 KΩ, ± 5 % resistor. What is the expected current? ( μa ) 35. A generator has an emf of 115 V, and an internal resistance of 0.1 ohms. Find the terminal voltage when it supplies a current of 50 A. (110 V) 36. A current source has o constant current of 5 A, and an internal resistance of 2 ohms. Find the terminal current when the voltage is 4 V. (3 A) 37. A battery has an open circuit terminal voltage of 28 V, and a short-circuit current of 200 A. Find the load current when the terminal voltage is 18 V. (71.4 A) 38. The terminal voltage of a d.c. source was found to be 150 V when it was supplying a load resistor of 25 K-ohms. The short-circuit current is 10 ma. Find the terminal voltage and current for a load resistor of 35 K-ohms. (181 V, 5.17 A) 39. The no load voltage of a small battery is 1.5 V. When a 2 K-ohm resistor is connected across the battery terminals, the current is 0.4 ma. Find the load voltage when a 900 ohm resistor is connected to the battery. (0.51 V) 40. a d.c. source was tested, and was found to supply 3 A at 120 V, and 5 A at 100 V. What current will it supply to a 65 ohm resistor? (2 A) - 6 -

7 41. A d.c. source was tested, and was found to supply 0.93 A to a 33 ohm load, and 0.55 A to an 82 ohm load. Find the voltage that would appear across a 63 ohm load resistor. (41.17 V) 42. When connected to a certain load resistor, the terminal voltage and current of a d.c. source were found to be 150 V and 2 A reactively. The open circuit voltage of the source is 200 V. Determine the terminal voltage and current when the source is loaded by a 50 ohm resistor. (133.3 V, 2.67 A) 43. When a voltmeter is connected across a given battery, it reads 2.5 V. When an ammeter is connected across the battery, it reads 500 ma. The resistance of the voltmeter is 0.2 K-ohms, and the resistance of the ammeter is 300 m-ohms. Find the battery parameters: E, I o, R o, and G o. (2.56 V, 531 ma, 4.82 ohms, 207 m-mho) 44. In the figure shown, when the switch is in position 1, the ammeter reading is 2.5 A; when in position 2, the voltmeter reading is 150 V. Find the source parameters E, I o, R o, and G o if (a) the two meters are ideal, and if (b) the ammeter and voltmeter resistances are 3 ohms and 2 K-ohms respectively. (R o = 60 ohms, ohms) - 7 -

CHAPTER 3: ELECTRIC CURRENT AND DIRECT CURRENT CIRCUIT

CHAPTER 3: ELECTRIC CURRENT AND DIRECT CURRENT CIRCUIT PSPM II 2005/2006 NO. 3 3. (a) Write Kirchhoff s law for the conservation of energy. FIGURE 2 (b) A circuit of two batteries and two resistors is