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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.
 Spring '12
 bkav

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