Page 117 - MATLAB an introduction with applications

102 ——— MATLAB: An Introduction with Applications

1 RR R
Therefore, R = = 12 3 .
1 + 1 + 1 RR + R R + R R
3 1
2 3
12
R 1 R 2 R 3

2.3 KIRCHHOFF’S LAWS

Kirchhoff’s laws are the two most useful physical laws for modeling electrical systems. It is necessary to
apply Kirchhoff’s laws in solving electric circuit problems as they involve many electromotive forces such
as resistance, capacitance and inductance.
The Kirchhoff’s laws are stated as follows:
1. Kirchhoff’s current law (node law): The algebraic sum of all the currents flowing into a junction (or
node) is zero (node analysis).
In other words, the sum of currents entering a node is equal to the sum of the currents leaving the same
node. A node is an electrical circuit is a point where three or more wires are joined together. Currents going
toward a node are considered positive while currents leaving a node are treated as negative.
The algebraic sum of all currents (in) a circuit node is zero. That is,
∑ () = 0
i
in
n
n
Referring to Fig. 2.9, Kirchhoff’s current law states that
i 2
i 3
i 1
i 2
i 2 i 2 i 4
i 6
i 1
i 1 i 3 i 3 i 1 i 3 i 5
(a) (b) (c) (d)
Fig. 2.9
Fig. 2.9 (a) i 1 + i 2 + i 3 =0
Fig. 2.9 (b) – (i 1 + i 2 + i 3 )= 0
Fig. 2.9 (c) i 1 + i 2 – i 3 =0
Fig. 2.9 (d) i 1 – i 2 – i 3 + i 4 + i 5 – i 6 =0

2. Kirchhoff’s voltage law (loop law): The algebraic sum of all the potential drops around a closed loop
(or closed circuit) is zero (loop analysis).
In other words, the sum of the voltage drops is equal to the sum of the voltage rises around a loop. That
is, the sum of all voltage drops around a circuit loop is zero. Hence

ΣV drop = 0
or ΣV gain = 0

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