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ECE CHAPTER 2 - Series Resistances Req = R1 R2 R3 Rn...

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Series Resistances - R eq = R 1 + R 2 + R 3 + … + R n Parallel Resistances - 1/R eq = 1/R 1 + 1/R 2 + 1/R 3 + … + 1/R n - Only for two resistances: R eq = R 1 R 2 /(R 1 + R 2 ) Load: an element (such as a toaster or light bulb) that absorbs power Electrical Network: Consists of circuit elements (such as resistances, voltage sources and current sources) connected together to form closed paths Network analysis: The process of determining the current, voltage, and power fro each element given the circuit diagram and the element values - Steps: 1. Locate a combination of resistances that are in series or parallel. (Often start farthest from the source) 2. Redraw the circuit with the equivalent resistance 3. Repeat steps 1 and 2 until the circuit is reduced as far a possible. 4. Solve for the currents and voltages in the final equivalent circuit. Then, transfer results back one step and solve for additional unknown currents and voltages. Repeat until all of the currents and voltages are known in the original circuit. Voltage Division (series) - Voltage-division principle : Of the total voltage, the fraction that appears across a given resistance in a series circuit is the ration of the given resistance to the total series resistance. - v 1 = R 1 i = v total R 1 /(R 1 + R 2 + R 3 ) - v 2 = R 2 i = v total R 2 /(R 1 + R 2 + R 3 ) - v 3 = R 3 i = v total R 3 /(R 1 + R 2 + R 3 ) - Any number of resistances Current Division (parallel) - Current-division principle : For two resistances in parallel, the fraction of the total current flowing in a resistance is the ratio of the other resistances to the sum of the two resistances. - i 1 = v /R 1 = i total R 2 /(R 1 + R 2 ) - i 2 = v /R 2 = i total R 1 /(R 1 + R 2 ) Node-Voltage Analysis - Selecting the reference node - Node: a point at which two or more circuit elements are joined together - Select one end of a voltage source as the reference node (ground node) - Assigning node voltages - The negative reference polarity of each of the node voltages is at the reference node
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- Finding element voltages in terms of the node voltages - Use KVL to find voltages and then Ohm’s law and KCL for current - If one end of an element is connected to the reference node, the voltage across the element is a node voltage - Writing KCL equations in terms of the node voltages - The advantage in selecting the reference node at one end of an independent
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