OhmGÇÖs and KirchhoffGÇÖs Laws Simple Circuits

OhmGÇÖs and KirchhoffGÇÖs Laws Simple Circuits

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Ohm’s and Kirchhoff’s Laws: Simple Circuits Introduction The circuits in this set of problems are called simple circuits because 1. Each circuit consists of a small number of circuit elements. 2. Each circuit consists only of resistors, voltage sources, current sources, and either a voltmeter or ammeter. 3. The voltages of the voltage sources and currents of the current sources have constant values. The inputs to these circuits are the voltages of the voltage sources and/or the currents of the current sources. The output of each circuit is either a voltage measured by a voltmeter or a current measured by an ammeter. All of the inputs have constant values. Consequently, the outputs also have constant values. Use Ohm’s and Kirchhoff’s laws to solve these problems. In particular, it’s important to notice that Ohm’s law applies to a current and voltage that adhere to the passive convention. Ohm’s law is discussed in Section 2.6 of Introduction to Electric Circuits by R.C. Dorf and J.A Svoboda. Kirchhoff’s laws are discussed in Section 3.3. Voltage and current sources are described in Section 2.6. Voltmeters and ammeters are described in Section 2.7. The passive convention is described in Section 1.6. Worked Examples Example 1: Consider the circuit shown in Figure 1. Find the value of the resistance, R . Find the power supplied by each source and the power absorbed by the resistor. Figure 1 The circuit considered in Example 1. 1
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Solution: Figure 2 shows the circuit from Figure 1 after replacing the voltmeter by an equivalent open circuit and labeling the voltage measured by the voltmeter. Label the element currents and voltages as shown in Figure 3. In anticipation of using Ohm’s law, the reference directions of the resistor current and voltage have been chosen to adhere to the passive convention. Consequently, the product of the resistor current and voltage is the power absorbed by the resistor, as required. The reference direction for the voltage source current has been selected so that the voltage source current and voltage do not adhere to the passive convention. Consequently, the product of the voltage source current and voltage is the power supplied by the voltage source, as required.
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This note was uploaded on 09/30/2010 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Tech.

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OhmGÇÖs and KirchhoffGÇÖs Laws Simple Circuits

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