Transformers

Problem 613: The maximum flux density in the core of a 3000/240-V, 50 Hz single-phase distribution transformer is 1.25 Tesla. If the voltage induced per turn is 8 volts, determine the cross sectional of the core in cm².

Problem 614: The net cross section of a transformer is 20 square inches. The maximum flux density is 11 kilogausses. The frequency is 60 Hz. If there are 1,000 turns in the primary, determine the primary induced emf.

Problem 615: Calculate the total magnetic flux in a 60-cycle transformer in which the induced emf per turn of the winding is equal to 2 V.

Problem 616: The low side of a certain welding transformer has 2 turns and delivers 300 A. If the high voltage side has 30 turns, how much current flows through it?

Problem 617: A single-phase transformer is rated 4,160 V primary and 250 V secondary. It has 1,500 turns in the primary and a voltage regulation of 8%. What should be the number of turns in the secondary winding?

Problem 618: The current densities in the primary and secondary windings of a step down transformer are 1250 and 1500 A per square inch, respectively. The ratio of transformation is 10:1 and the mean length per turn of the primary is 15% greater than that of the secondary. If the primary winding resistance is 20 ohms, calculate the resistance of the secondary windings.

Problem 619: A certain transformer has a ratio of 8 is to 1. The primary winding resistance is 0.00283 ohm per turn and has 1155 more turns than the secondary winding. If the copper losses in the primary is 20% less than in the secondary, find resistance of the secondary winding.

Problem 620: A 10 kVA, 2400/240-V single-phase transformer has the following resistances and reactances: \(r_1=3\,\Omega\), \(x_1=15\,\Omega\), \(r_2=0.03\,\Omega\), \(x_2=0.150\,\Omega\). Find the primary voltage required to produce 240 V at the secondary terminals at full load, when the power factor is 0.8 lagging.

Problem 621: A 10-kVA, 2,000/400 V, single-phase distribution transformer has a primary and secondary winding impedances of 5.0 + j10 and 0.2 + j0.45 ohms, respectively. Calculate the voltage across the secondary terminals at full load, 80% power factor lagging, when the primary is supplied with 2,000 volts?

Problem 622: A single-phase transformer rated 75 kVA, 8000 volts primary 240 volts secondary, is given the short circuit test. With the secondary terminals short-circuited, 440 volts (60 Hz) is impressed on the primary, which then draws rated current and 1125 watts. Solve for the percentage impedance of the transformer.

Problem 623: A short circuit test was performed upon a 10-kVA, 2300/230 volt transformer with the following results: \(E_{sc}\) = 137 volts; \(P_{sc}\) = 192 W; \(I_{sc}\) = 4.34 A. Calculate in primary terms the reactance of the transformer.

Problem 624: A single-phase, 25 kVA, 4800/240 volt transformer was given a short circuit tests: With the secondary terminals short-circuited, 93.75 volts was applied on the primary so that the ammeter reads rated current and the wattmeter reads 162.74 watts, all on the primary side. Solve for the percentage resistance of the transformer.

Problem 625: The following data were obtained when a short circuit test was performed upon a 100 kVA, 2400/240 volts distribution transformer: \(E_{sc}\) = 72 volts; \(I_{sc}\) = 41.6 A; \(P_{sc}\) = 1,180 W. All instruments are on the high side during the short circuit test. Calculate the equivalent resistance and reactance of the transformer.

Problem 626: A 13.8 kV/480 V, 10 MVA three-phase transformer has 5% impedance. What is the impedance in ohms referred to the primary?

Problem 627: A short circuit test was performed on a 20 kVA, 2000/200 V single-phase transformer. With the secondary winding short circuited, full load current flows in the primary winding with 100 V applied on it. The wattmeter connected in the primary read 300 W. Determine the terminal voltage on full load unity pf.

Problem 628: The following data were obtained when a short circuit test was performed upon a 100 kVA, 2400/240 volts distribution transformer: \(E_{sc}\) = 72 volts; \(I_{sc}\) = 41.6 A; \(P_{sc}\) = 1,180 W. All instruments are on the high side during the short circuit test. Calculate the percent regulation at a power factor of 0.75 lagging.

Problem 629: A 200-kVA transformer with impedance of 5% and the power factor of the load is 85%. The primary voltage is 6,000 volts while the copper loss is 5 kW. Find the percentage regulation.

Problem 630: A 150 kVA, three-phase transformer supplies 100 kVA at 50% lagging power factor. The transformer's winding impedance is 2% resistance and 5% reactance, based on 150 kVA. Determine the voltage regulation of the transformer at this load. Assume 100% voltage.

Problem 631: A short circuit test was performed upon a 10-kVA, 2300/230 volt transformer with the following results: \(E_{sc}\) = 137 volts; \(P_{sc}\) = 192 W; \(I_{sc}\) = 4.34 A. Calculate the percent regulation at a lagging power factor of 0.707.

Problem 632: A 100 kVA, 6600/600 V, 60 Hz single-phase transformer operating at rated condition has the following losses: hysteresis loss = 520 W; eddy current loss = 370 W and copper loss = 2000 W. If this transformer is to be used on a 50 Hz system, determine its new kVA rating. Assume the same total losses and maximum core flux.