Problems

Author: E.E. Kimberly

	Problem	Answer
1	The efficiency of a single-phase, 10-kv-a, 2200/220-volt, 60-cycle transformer is to be measured by loading. Show by a diagram the proper locations of all necessary meters, and specify the required ranges of all instruments.
2	The single-phase transformer of Problem 1 has a primary resistance of 3.0 ohms, a secondary resistance of 0.03 ohm, and a no-load power input of 100 watts. Calculate the energy efficiency in a period of 24 hours on the following load schedule: 4 hours full load at 90% power factor; 2 hours 1/2 rated load at 100% power factor; 18 hours no load. The exciting current may be neglected.
3	Show by a diagram a three-phase group of single-phase transformers connected Y-A. Let the transformers be similar, except that one is of additive-polarity and two are of subtractive polarity.
4	Specify the voltage ratio for each of a group of three single-phase transformers to be used to "step down" Y-Δ from a three-phase 2200-volt line to 220 volts for factory service.
5	Specify the voltage ratios and kv-a capacities of two single-phase transformers to "step down" from 2200 volts to 220 volts, three-phase, by open-delta connection to supply a 175-kv-a load.
6	An auto-transformer is to be used to "step down" a voltage of 220 volts to 120 volts. The load current is to be 50 amp. Neglecting the exciting current, find the current in each part of the transformer.
7	A 2300/230-volt, 10-kv-a, single-phase transformer has an effective resistance of 2% and a leakage reactance of 1%, Calculate the regulation at full load at 60% power factor leading.
8	Calculate the regulation of the transformer of Problem 7 with 80 per cent of full load at 60% power factor lagging.
9	A 50-kv-a, 60-cycle, 2300/230-volt transformer is to be used on a 25-cycle line as a temporary expedient. What would be the approximate maximum voltage permissible on the 2300-volt winding?
10	An anthracite mine has the following 3-phase, 60-cycle motors: two 100-hp induction motors with estimated efficiency of 90% and power factor of 91% lagging; five 50-hp induction motors with estimated efficiency of 82% and power factor of 78% lagging; three 100-hp synchronous motors with estimated efficiency of 88% and power factor of 80% leading. The available transmission line is 3100-volt, 60-cycle, 3-phase. Write purchase specifications for three single-phase transformers to step down the voltage to 440 volts by a Y-A connection for the motors. Assume a load diversity factor of 69%.
11	A transformer has a full-load voltage of 108 volts and a no-load voltage of 115. What is the regulation in per cent? Assume constant primary voltage.
12	A balanced three-phase load of 1740 kv-a is to be supplied by two transformers connected open delta. What must be the single-phase kv-a rating of each transformer?
13	An auto-transformer for starting an induction motor steps down the line voltage from 230 volts to 84 volts per phase line-to-neutral for the motor. If the transformer furnishes 20 kv-a per phase at 50% power factor, calculate the primary and the secondary currents in the auto-transformer. Neglect the exciting current.
14	What would be the maximum permissible continuous kw output at unity power factor, three-phase, from two similar 100-kv-a single-phase transformers connected in T to a two-phase line?
15	Two 100-kv-a, 2400/480-volt transformers are connected in open delta for a three-phase load of unity power factor. How many kilowatts of power can be delivered to the load without overloading the transformers?	174 kw
16	A welding transformer operating from a 240-volt line has 500 turns in its primary winding and 1 turn in its secondary winding. When the transformer during a welding cycle draws 20 amp from the line, approximately how many amperes are flowing in the weld?	10000 amp
17	A 100-kv-a, single-phase, 2400/240-volt, 60-cycle transformer has an iron loss of 1200 watts at rated voltage and a copper loss of 1500 watts at rated current. If it is assumed that 80 per cent of the iron loss is caused by eddy currents, what will be the approximate efficiency at rated-load current when supplying a resistance load from a 25-cycle power line of 1000 watts?	95.8%
18	Under the conditions of Problem 17, the iron losses are abnormally low but the transformer's heat-dissipative capacity is as great as ever. What per cent of increase in rated-load current is permissible, if the operating temperature is not to exceed that for which the transformer was designed?	24.8%