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Circuit Theorems
• From the previous section, we have
discovered that Kirchhoff's law is a powerful
technique in analysing circuit without
changing its configuration
...


• In order to handle this complexity, engineers
over the years have developed some
theorems to simplify circuit analysis
...

• Before we look at these two theorems, let’s
quickly study superposition theorem
...

• However, to apply the superposition principle,
we must keep two things in mind:

1
...
This implies that we replace every
voltage source by 0 V (or a short circuit), and
every current source by 0 A (or an open
circuit)
...

2
...
With
these in mind, we apply the superposition
principle in three steps:

Steps to Apply Superposition Principle
1
...
Find the output (voltage or current)
due to that active source using the
techniques covered in previous sections
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Repeat step 1 for each of the other
independent sources
...
Find the total contribution by adding
algebraically all the contributions due to the
independent sources
...

• For this reason, it is not applicable to the
effect on power due to each source, because
the power absorbed by a resistor depends on
the square of the voltage or current
...


Ex
• Use the superposition theorem to find the
value of variables specified in the following
circuits
...
(a)

Fig
...
(c)

Fig
...
(d)

Fig
...

• As a typical example, a household outlet
terminal may be connected to different
appliances constituting a variable load
...


• To avoid this problem, Thevenin’s theorem
provides a technique by which the fixed part
of the circuit is replaced by an equivalent
circuit
...
(a) can be
replaced by that in Fig
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• The load in Figure above may be a single
resistor or another circuit
...
(b) is known as the Thevenin equivalent
circuit;

Thevenin’s Theorem
• Thevenin’s theorem states that a linear twoterminal circuit can be replaced by an
equivalent circuit consisting of a voltage
source VTh in series with a resistor RTh, where
VTh is the open-circuit voltage at the terminals
and RTh is the input or equivalent resistance at
the terminals when the independent sources
are turned off

• Thevenin’s theorem is very important in circuit
analysis
...

• A large circuit may be replaced by a single
independent voltage source and a single
resistor
...
below, to the left of the
terminals a-b
...


The circuit becomes what
is shown in Fig
...

Thus,

Fig
...
(b)
...
(b)

Alternatively, it is even
easier to use nodal
analysis
...

At the top node, KCL gives

• The Thevenin equivalent
circuit is shown in Fig
...

• The current through RL is

When RL = 6 Ω
Fig
...
Then
find I
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• The circuit in Fig
...
(b)
...


• We find RN in the same
way we find RTh in the
Thevenin equivalent
circuit
...

• This leads to the circuit
in Fig
...
Thus

• To find IN, we short-circuit terminals a and b,
as shown in Fig
...

• We ignore the 5Ω resistor because it has been
short-circuited
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