# For example the current sources shown in fig 218a can

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Unformatted text preview: parallel. The combined current is the algebraic sum of the current supplied by the individual sources. For example, the current sources shown in Fig. 2.18(a) can be combined as in Fig. 2.18(b). The combined or equivalent current source can be found by applying KCL to node a . IT + I2 = I1 + I3 | Textbook Table of Contents | Problem Solving Workbook Contents CHAPTER 2 Basic Laws 37 or IT IT = I1 − I2 + I3 (2.18) A circuit cannot contain two different currents, I1 and I2 , in series, unless I1 = I2 ; otherwise KCL will be violated. Kirchhoff ’s second law is based on the principle of conservation of energy: a I2 I1 I3 b (a) IT a Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero. IS = I1 – I2 + I3 b (b) Expressed mathematically, KVL states that Figure 2.18 M vm = 0 (2.19) Current sources in parallel: (a) original circuit, (b) equivalent circuit. m=1 where M is the number of voltages in the loop (or the number of branches in the loop) and vm is the mth voltage. To illustrate KVL, consider the circuit in Fig. 2.19. The sign on each voltage is the polarity of the terminal encountered ﬁrst as we travel around the loop. We can start with any branch and go around the loop either clockwise or counterclockwise. Suppose we start with the voltage source and go clockwise around the loop as shown; then voltages would be −v1 , +v2 , +v3 , −v4 , and +v5 , in that order. For example, as we reach branch 3, the positive terminal is met ﬁrst; hence we have +v3 . For branch 4, we reach the negative terminal ﬁrst; hence, −v4 . Thus, KVL yields (2.20) + (2.21) − v 2 + v 3 + v 5 = v1 + v 4 v2 + Rearranging terms gives v3 − −v1 + v2 + v3 − v4 + v5 = 0 KVL can be applied in two ways: by taking either a clockwise or a counterclockwise trip around the loop. Either way, the algebraic sum of voltages around the loop is zero. − + v1 + − v4 which may be interpreted as v5 + − Sum of voltage drops = Sum of voltage rises (2.22) Figure 2.19 This is an alternative form of KVL. Notice that if we had traveled counterclockwise, the result...
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## This note was uploaded on 07/16/2012 for the course KA KA 2000 taught by Professor Bkav during the Spring '12 term at Cambridge.

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