ECE22 Delta - Wye and Wye - Delta Transformation Experiment OBJECTIVE This experiment explores the Delta - Wye and Wye - Delta transformation, and how can this be used to simplify the analysis of circuits. DISCUSSION In solving networks (having considerable number of branches), one sometimes experiences great difficulty due to many simultaneous equations that must be solved. However, such complicated network can be simplified by successively replacing delta meshes by equivalent wye system and vice versa. Suppose we are given three resistors R12, R23 and R31 connected in delta fashion between terminals 1, 2 and 3. So far as the respective terminals are concerned, these three given resistances can be replaced by the three resistances R1 , R2 and R3 connected in Wye . Delta Wye Delta-Wye Transformation To convert from Delta to Wye, we use the following equations: Wye-Delta Transformation To convert from Wye to Delta, we use the following equations: PROCEDURE Wye – Delta Transformation Construct the circuit shown below. Assume that R1 = 2 kΩ, R2 = 1 kΩ, R3 = 1.5 kΩ, Ra = 2.5 kΩ, Rb = 500 Ω, and Rc = 1 kΩ. Ia Ra Ib Rc Rb Ic Set the DC supply output voltage control to minimum then connect it to the circuit. Switch the DC supply ON and set its voltage to Vs = 10 Volts. Use the current divider rule to calculate the theoretical currents Ia, Ib, and Ic and to evaluate the theoretical voltage drop Vad, Vbd, and Vcd. Record your answers in the theoretical part on designated tables. Using a voltmeter, measure the voltage drop Vad, Vbd, and Vcd, and record the values in the table below. Pay attention to polarity. Voltage Drop Vad (V) Measured Theoretical Vbd (V) Measured Theoretical Vcd (V) Measured Theoretical Use an ammeter to measure the DC currents Ia, Ib, and Ic, and record the values in the table below. Pay attention to polarity. Current Ia (mA) Measured Theoretical Ib (mA) Measured Theoretical Ic (mA) Measured Theoretical Convert the Wye connection in the above circuit into a Delta connection and draw the resulting circuit below. Delta – Wye Transformation Now construct the circuit shown below. Assume that R1 = 2 kΩ, R2 = 3 kΩ, R3 = 5 kΩ, R4 = 10 kΩ, R5 = 1.5 kΩ and R6 = 1 kΩ. I1 R1 R4 R2 R3 I5 R6 R5 I6 Set the DC supply output voltage control to minimum then connect it to the circuit. Switch the DC supply ON and set its voltage to Vs = 10 Volts. Calculate the theoretical voltage drop Vad, Vbd, and Vcd and theoretical currents I1, I5, and I6. Record your answers in the theoretical part of the table Using a voltmeter, measure the voltage drop Vad, Vbd, and Vcd, and record the values in the table below. Pay attention to polarity. Voltage Drop Vad (V) Measured Theoretical Vbd (V) Measured Theoretical Vcd (V) Measured Theoretical Use an ammeter to measure the DC currents I1, I5, and I6, and record the values in the table below. Pay attention to polarity. Current I1 (mA) Measured Theoretical I5 (mA) Measured Theoretical I6 (mA) Measured Theoretical Convert the Delta connection in the above circuit into a Wye connection and draw the resulting circuit below. Guide Questions 1. Are the results in Delta - Wye Tables (Voltage Drop and Current) close to the values in Tables Wye – Delta? Why? 2. How does the given circuit in Wye – Delta Transformation differs from the sketch made in Delta – Wye Transformation? 3. How can Delta – Wye transformation and vice versa important on determining the voltage drops and currents in a circuit? END