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Sheet (3) Transformers 1) A transformer has turns ratio of 5. If a 100 Ω resistor is connected across the secondary, what is the resistance referred to the primary? If the same resistor is instead connected across the primary, what is its resistance referred to the secondary? 2) The parameters of the equivalent of a transformer, having a turns ratio of 5, are R1=0.5Ω, R2=0.021Ω, X1=3.2Ω, X2=0.12Ω, Rc=350Ω referred to primary, and Xm=98Ω referred to primary. Draw the approximate equivalent circuit of the transformer, referred to a) the primary and b) the secondary. Show the numerical values of the circuit parameters. 3) The results of open circuit and short circuit tests on a 25kVA, 440V/220V, 60 Hz transformer are as follows: Open-circuit test: high-voltage side is open circuited, input voltage= 220V, input current= 9.6A, input power =710W. Short-circuit test: low-voltage short-circuited, input voltage=42V, input current =57A, input power 1030W. Obtain the exact equivalent circuit parameters, referred to the high voltage side. 4) For the test data of problem (3) obtain the values of the circuit constants for the approximate equivalent circuit referred to the low voltage side. 5) Open circuit and short circuit tests are performed on a 10kVA, 220V/110V, 60 Hz transformer, both tests are performed with the instrument on the high-voltage side, and the following data are obtained: Open-circuit test: input voltage= 220V, input current= 3.16A, input power =500W. Short-circuit test: input voltage=65V, input current =10A, input power 400W. Obtain the approximate equivalent circuit, referred to the a) high voltage side, and b) low voltage side. 6) The parameters of the equivalent of 150kVA, 2400V/240V transformer, are R1=0.2Ω, R2=2mΩ, X1=0.45Ω, X2=4.5mΩ, Rc=10kΩ referred to primary, and Xm=1.55kΩ referred to primary. using the approximate equivalent circuit referred to the primary side, when the transformer is operating at rated load and rated voltage with 0.8 lagging power factor determine: a) Voltage regulation. b) The transformer power loss. c) Efficiency. 7) The parameters of the equivalent of 110kVA, 2200V/110V transformer, are R1=0.22Ω, R2=0.5mΩ, X1=2Ω, X2=5mΩ, Rc=5494.5Ω referred to primary, and Xm=1099Ω referred to primary. using the approximate equivalent circuit referred to the primary side, when the transformer is operating at full load with unity power factor determine: a) Voltage regulation. b) The transformer power loss. c) Efficiency.

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