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Unformatted text preview: EECS 314 Fall 2007 HW 04 Problem 1 Student's name ___________________________ Discussion section # __________ (Last name, first name, IN INK) © 2007 Alexander Ganago Page 1 of 4 The Big Picture Equivalent sources The voltage source V S in series with a resistor R S , as shown on the left top and on the center top diagrams, is equivalent to the current source I S in parallel with the same resistor R S , shown on the right top diagram, provided that V S = I S ⋅ R S . The voltage source with a resistor in series is called Thevenin circuit while the equivalent current source with the same resistor in parallel is called the Norton circuit. The equivalent sources such as shown above are NOT IDENTICAL. For example, if nothing is connected to the terminals a and b of either source, the voltage source does not absorb or supply any power but the current source supplies (I S ) 2 ⋅ R S – all this power is absorbed in the resistor. It is only for the load connected to the terminals a and b that the sources are equivalent: their voltagecurrent characteristics are the same. Namely, for all possible load resistances R L , the voltage V across the load and the current I through the load (see the circuit diagrams on the right) fall on the same straight line (see the sketch above), which connects the opencircuit voltage V S (at zero current) and the shortcircuit current I S (at zero voltage). Source transformation Replacing a source with its equivalent is called “source transformation”; it helps to solve many circuit problems, especially the “ladder” circuits such as shown on the next page. EECS 314 Fall 2007 HW 04 Problem 1 Student's name ___________________________ Discussion section # __________ (Last name, first name, IN INK) © 2007 Alexander Ganago Page 2 of 4 When you apply the source transformation carefully label which part of the circuit you are going to transform at each step, and it’s a good idea to redraw the circuit every time you replace a source with its equivalent. Note that, according to KCL, a parallel combination of current sources I 1 and I 2 with parallel resistors R 1 and R 2 is equivalent to one current source I 1 +I 2 and one resistor R 1  R 2 . Also, according to KVL, a series combination of voltage sources V 1 and V 2 with series resistors R 1 and R 2 is equivalent to one voltage source V 1 +V 2 and one resistor R 1 +R 2 . For example, source transformation can be used to reduce the circuit below to its Thevenin or Norton equivalent. The first step in this sample solution involves the transformation of the 12V source into its Norton equivalent as shown here. EECS 314 Fall 2007 HW 04 Problem 1 Student's name ___________________________ Discussion section # __________ (Last name, first name, IN INK) © 2007 Alexander Ganago Page 2 of 4 When you apply the source transformation carefully label which part of the circuit you are going to transform at each step, and it’s a good idea to redraw the circuit every time...
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 Fall '07
 Ganago
 Volt, Thévenin's theorem, Voltage source, Alexander Ganago

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