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# Problems

Author: E.E. Kimberly

 Problem Answer 1 Plot accurately on 1/10-in. cross-section paper a sinusoidal current whose maximum value is 3 amperes. Plot on the same axes a curve of current squared. Demonstrate that the square root of the average ordinate of the i2 wave is 0.707 times the maximum ordinate of the i wave. 2 Determine the average value and the maximum value of one half-cycle (starting at zero value) of a sinusoidal alternating current which will produce heat in a resistor at the same average rate as a direct current of 30 amperes. 3 A 100-turn coil is rotated in a uniform magnetic field and generates a voltage at a frequency of 25 cycles. A voltmeter connected across the coil reads 30 volts. What is the maximum flux enclosed by the coil? 4 A 200-turn coil in the form of a 6 in. x 6 in. rectangle rotates at 3600 rpm in a uniform field of 50,000 lines per sq in. Calculate the instantaneous emf when the coil is 60 deg past the point of zero voltage. 5 What is the maximum value of a sine wave of voltage which would produce heat in a resistor at the same average rate as 100 volts of direct current? 6 As indicated in the diagram, five lamps rated at 75 watts, 115 volts are connected in parallel with two lamps rated at 200 watts, 115 volts across a two-wire, 115-volt line. Calculate the line current. 6.73 amp 7 A 100-watt, 115-volt lamp is connected in series with a 500-watt, 115-volt smoothing iron across a two-wire, 230-volt circuit. Calculate the voltage applied to each. Calculate the power in each. Lamp, 191.8V; Iron, 38.4VLamp, 278W; Iron, 55.6W 8 A 25-watt, 115-volt lamp is connected in series with a 200-watt, 115-volt lamp across a 230-volt supply line. How many 25-watt, 115-volt lamps placed in parallel with the first one will cause the 200-watt lamp to light to normal brilliance? 9 A 120-volt voltmeter has a resistance of 60,000 ohms. How much resistance must the series multiplier for this meter have to make it a 600-volt meter? How much current would the meter then draw from a 600-volt circuit? 10 The resistance of a resistor of about 4000 ohms is to be found by using a voltmeter having a resistance of 60,000 ohms. What per cent of error would be introduced by the current taken by the voltmeter? The voltmeter is connected directly across the resistor. 11 If the voltmeter of Problem 10 were connected to include the ammeter and the ammeter resistance is 0.001 ohm, what per cent of error in the measurement would be introduced by the ammeter resistance? 12 If all of the shunt field coils of the generator of Fig. 10-12 are connected in series across a 600-volt bus, what would be the voltage across each coil? 13 A series street-lighting circuit has 75 lamps rated at 6.6 amperes, 225 watts. The line resistance is 50 ohms. How many volts must be supplied by the supply transformer? 14 A compound generator whose full-load current is 50 amperes compounds its voltage too much. The series field, which has a resistance of 0.06 ohm, is to be relieved of 25 per cent of its current by means of a "diverter" or parallel resistor. What must be the resistance of the diverter? 15 Four shunt field coils as shown in Fig. 10-13 have a combined resistance of 100 ohms. If they were connected in parallel, what would be their combined resistance? 16 A lighting load of 100 lamps, each rated at 100 watts at 120 volts, is to be supplied over a two-wire system each wire of which has a resistance of 0.1 ohm. What must be the voltage at the generator to insure rated voltage at the lamps? 136.6 17 Calculate the voltages that would appear across RL1 and across RL2 of Example 3-7 if the middle wire were removed? IaRL1 = 98.0; IlRL2 = 147 18 Assume that RL1 of Fig. 3-7 is adjusted until Ia is 14 amperes and that at the same time RL2 is adjusted until Ib, is 10 amperes. What will then be the voltages across RL1 and across RL2? 19 Assume that in the circuit of Fig. 3-7 the resistor Rm is disconnected and the middle line is left open. What voltage will then appear between the mid-point between the generators and the point M of the circuit? 20 A three-wire, 120/240-volt feeder of 2/0 conductor to an isolated machine shop is 250 ft long. How many kilowatts can be drawn from the two outside conductors by the shop motors alone without causing a loss of more than 10 volts in the line? How many kilowatts can be drawn from one side of the system only without causing a line voltage drop in excess of 10 volts. See the Appendix for the resistance per 1000 feet of 2/0 conductor. 21 If in Fig. 3-7 the current in RLI is 6.43 amperes and that through RL2 is 4.35 amperes and the resistance of each line is 0.4 ohm, what is the voltage across the terminals of each generator? 22 What is the effective voltage generated in the coil of Problem 14, Chapter 2?

Last Update: 2011-02-25