The foundations
of network theory were laid about 150 years ago by Gustav Kirchhoff, a German
university professor, whose careful experiments resulted in the law that bear
his names. In the following discussion, a branch is a part of a circuit with
two terminals to which connections can be made, a node is the point where two
or more ranches come together, and a loop is a closed path formed by connecting
branches.
of network theory were laid about 150 years ago by Gustav Kirchhoff, a German
university professor, whose careful experiments resulted in the law that bear
his names. In the following discussion, a branch is a part of a circuit with
two terminals to which connections can be made, a node is the point where two
or more ranches come together, and a loop is a closed path formed by connecting
branches.
Kirchhoff’s
Current Law
Current Law
To repeat
Kirchhoff’s experiments in the laboratory, we could arrange to measure the
current in a number of conductors or leads soldered together
Kirchhoff’s experiments in the laboratory, we could arrange to measure the
current in a number of conductors or leads soldered together
In every
case, we would find that the sum of the current flowing into the common point
(a node) at any instant is just equal to the sum of the currents flowing out.
case, we would find that the sum of the current flowing into the common point
(a node) at any instant is just equal to the sum of the currents flowing out.
In the
figure above, a circuit model is used to represent an actual connection. The
arrows define the reference direction for positive current where current is
defined by the motion of positive charges. The quantity ‘i1’
specifies the magnitude of the current and its algebraic sign with respect to
the reference direction. If i1 has a value of ‘+5A’, the effect is
as if positive charge is moving towards the node at the rate of 5C/s. If i1
= +5A flows in a metallic conductor in which charge is transported in the form
of negative electrons, the electrons are actually moving away from the node but
the effect is the same. If I2 has a value of ‘-3A’, positive charge
is in effect moving away from the node. In a practical situation the direction
of current flow is easy to determine; if an ammeter reads ‘upscale’, current is
flowing from the meter terminal marked (+) through the meter to the terminal
marked (-).
figure above, a circuit model is used to represent an actual connection. The
arrows define the reference direction for positive current where current is
defined by the motion of positive charges. The quantity ‘i1’
specifies the magnitude of the current and its algebraic sign with respect to
the reference direction. If i1 has a value of ‘+5A’, the effect is
as if positive charge is moving towards the node at the rate of 5C/s. If i1
= +5A flows in a metallic conductor in which charge is transported in the form
of negative electrons, the electrons are actually moving away from the node but
the effect is the same. If I2 has a value of ‘-3A’, positive charge
is in effect moving away from the node. In a practical situation the direction
of current flow is easy to determine; if an ammeter reads ‘upscale’, current is
flowing from the meter terminal marked (+) through the meter to the terminal
marked (-).
By
Kirchhoff’s current law, the algebraic sum of the currents into a node at any
instant is zero. It is sometimes convenient to abbreviate this statement, and
write ‘∑i = 0,’ where the Greek letter sigma stands for ‘summation.’ As applied
to the figure above b,
Kirchhoff’s current law, the algebraic sum of the currents into a node at any
instant is zero. It is sometimes convenient to abbreviate this statement, and
write ‘∑i = 0,’ where the Greek letter sigma stands for ‘summation.’ As applied
to the figure above b,
∑i = 0 = i1 + i2
– i3 + i4 (2.1)
– i3 + i4 (2.1)
Obviously
some of the currents may be negative.
some of the currents may be negative.
