Selection of our books indexed in the Book Citation Index in Web of Science™ Core Collection (bkci)

Figure 19. Node of circuit
Advances in Bioengineering
202

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Figure 20. Voltage and current convention
In describing a circuit, we define its characteristics with terms node, branch, path, closed path,
and mesh as follows:
• Node: A point at which two or more circuit elements have a common connection.
• Branch: A circuit element or connected group of circuit elements. A connected group of
circuit elements usually connect nodes together.
• Path: A connected group of circuit elements in which none is repeated.
• Closed Path: A path that starts and ends at the sam node.
• Mesh: A closed path that does not contain any other closed paths within it.
• Essential Node: A point at which three or more circuit elements have a common connection.
• Essential Branch: A branch that connects two essential nodes.
Kirchhoff’s current law could be also applied to any closed surface surrounding a part of the
circuit. It’s understood that the closed surface does not intersect any of the circuit elements.
3.2.2. Voltage
Voltage represents the work per unit charge associated with moving a charge between two
points (A and B in figure 20) and that is given as the following formula:
V =
dW
dt
The unit of measurement for voltage is the volt (V). A constant voltage source is denoted by
the letter V, while a time-varying voltage is denoted by the lowercase letter 
v(t)
, or just 
v
. In
figure 20, the voltage, 
υ
between two points (A and B) is the amount of energy required to
move a charge from point A to point B.
Kirchhoff’s Voltage Law
Kirchhoff’s voltage law is utilized to ensure the voltage relationship at any branch of circuit.
Starting from any point of circuit, the sum of potential drop at the closed branch along the
clockwise or counterclockwise direction is equal to the sum of potential rise.
Biomedical Sensor, Device and Measurement Systems
http://dx.doi.org/10.5772/59941
203

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Figure 21. Circuit loop
In figure 21, the reference direction of electromotive force, current and branch voltage is
marked. Cycling one circle along virtual line given in circuit, the following equation could be
listed out:
U
1
+ U
4
=U
2
+ U
3
Above equation could be also written into the following equation:
U
1
−U
2
−U
3
+ U
4
=0
Namely, 
∑
U =0
According to above voltage equation, the algebraic sum of branch voltage is equal to zero along
any a closed branch circuit. If it is stipulated that potential drop is negative, potential rise is
positive.
Kirchhoff’s laws are applied in electrical circuit analysis to determine unknown voltages and
currents. Each unknown variable has its distinct equation. To solve for the unknowns using
MATLAB, we create a matrix representation of the set of equations and solve them using the
matrix calculation techniques.