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## Oluwayomi Adamo Department of Electrical Engineering

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**EENG 2610: Circuits AnalysisClass 3: Resistor Combinations,**Wye-Delta Transformations, Dependent Sources Oluwayomi Adamo Department of Electrical Engineering College of Engineering, University of North Texas**Simplifying Resistor Combinations**• To determine equivalent resistance at a pair of terminals of a network • Begin at the end of the network opposite the terminals • Repeat the following two steps as needed to reduce the network to a single resistor at the pair of terminals • Combine resistors in series • Combine resistors in parallel**Resistor Specifications**• Resistor Value • Standard resistor values are usually fixed, so to achieve a specific value, we need to combine standard value resistors in a certain configuration. (see Table 2.1 on page 45) • Tolerance • Typically, 5% and 10%, which specifies possible minimum and maximum resistance values • Power Rating • Specifies the maximum power that can be dissipated by the resistor. Typically, ¼ W, ½ W, 1 W, 2 W, …**Example 2.22: Find the range for both current and power**dissipation in the resistor if R has a tolerance of 10%.**Analyzing Circuits with Single Source and Series-Parallel**Combination of Resistors • Step 1 • Systematically reduce the resistive network so that the resistance seen by the source is represented by a single resistor • Step 2 • Determine the source current for a voltage source or the source voltage if a current source is present • Step 3 • Expand the network, retracing the simplification steps, and apply Ohm’s law, KVL, KCL, voltage division, and current division.**Example 2.24: Find all the currents and voltages labeled in**the network**Wye-Delta Transformation**Can you simplify it? Equivalent Transform For two networks to be equivalent at each corresponding pair of terminals, it is necessary that the resistance at the corresponding terminals be equal.**Circuits with Dependent Sources**• Controlled sources are used to model many important physical devices • Problem Solving Strategy • When writing KVL and/or KCL equations for the network, treat the dependent sources as though it were an independent source. • Write the equation that specifies the relationship of the dependent source to the controlling parameter. • Solve the equations for the unknowns. Be sure that the number of linearly independent equations matches the number of unknowns. • Will see a lot of examples a little later.