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32 Sources and power for HW 03

32 Sources and power for HW 03 -...

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Ganago / Sources and Power / for HW 03 © 2010 Alexander Ganago Page 1 of 15 File: Sources and power for HW 03 6.1 Overly simplistic models for independent sources – why overly ? The circuit models for independent voltage sources (Figure 6‐1) and independent current sources (Figure 6‐2), although convenient for solving simple problems, are overly simplistic for several reasons. Obviously, they fail to predict how much power can be transferred from the source to the load. Figure 6‐1. The circuit model for independent voltage sources and its voltage‐current characteristic. Figure 6‐2. The circuit model for independent current sources and its voltage‐current characteristic.
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Ganago / Sources and Power / for HW 03 © 2010 Alexander Ganago Page 2 of 15 File: Sources and power for HW 03 Consider an independent voltage source connected to a load, as shown in Figure 6‐3, and assume that the load resistance is variable. Figure 6‐3. An independent voltage source connected to a load resistor. For example, assume that the source V S = 1.5 V serves as a model for AA‐type battery, and the load R L = 3 Ω represents a small incandescent lamp. Then the power absorbed by the load P L = V S ( ) 2 R L equals 0.75 W. If two identical lamps are connected in parallel, their equivalent resistance of 1.5 Ω plays the role of R L and the absorbed power increases to 1.5 W. If 10 lamps are connected in parallel, we obtain R L = 0.3 Ω , and the absorbed power P L = 7.5 W. Adding thousands lamps in parallel, we would have to conclude that a single battery would supply kilowatts of power, enough to illuminate a lecture room, which is of course absurd. The wrong conclusion results from the simplified circuit model. Similarly, load resistance R L connected to independent current source I S , as shown in Figure 6‐4, absorbs the power P L = I S ( ) 2 R L , which endlessly grows as R L gets larger; for example, if more and more lamps are connected in series. Again, an overly simplified model leads to absurd results.
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Ganago / Sources and Power / for HW 03 © 2010 Alexander Ganago Page 3 of 15 File: Sources and power for HW 03 Figure 6‐4. An independent current source connected to a load resistor. 6.2 Better models for the sources The circuit models for independent sources are greatly improved by addition of resistances R S – in series with a voltage source and in parallel with a current source. Think about these resistances as internal : they belong to the source and cannot be disconnected from it. For example, the whole complex chemistry of a battery can be approximately represented by a single parameter – its internal resistance R S ; function generators often have R S = 50 Ω . Figure 6‐5. The Thévenin equivalent circuit includes resistance R S connected in series with the voltage source V S .
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Ganago / Sources and Power / for HW 03 © 2010 Alexander Ganago Page 4 of 15 File: Sources and power for HW 03 Figure 6‐6. The Norton equivalent circuit includes resistance R S connected in parallel with the current source I S .
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