Solution:
We need to find the Thevenin resistance
R
Th
and the Thevenin
voltage
V
Th
across the
terminals
a
-
b
.
To get
R
Th
, we use the circuit in Fig. (a)
R
Th
= 2 + 3 + (6 // 12 )=5+(
6×12
6+12
)=5+4=9Ω
To get
V
Th
, we consider the circuit in Fig.(b).Applying mesh analysis,
−12 + 18i
1
− 12i
2
= 0
,
i
2
= −2 A,
Solving for i1, we get i
1
= −2
/
3.
Applying KVL around the outer loop to get
V
Th
across terminals
a
-
b
, we obtain,
−12 + 6i
1
+ 3i
2
+ 2(0) + V
Th
= 0
V
Th
= 22 V
For maximum power transfer,
R
L
=
R
Th
= 9Ω and the maximum power is,
𝑃
𝑀𝐴𝑋
=
𝑉
𝑇𝐻
2
4𝑅
𝐿
=
22×22
4×9
=
13.44W
Superposition Theorem:
The principle of superposition helps us to analyze a linear circuit with more than
one current or voltage sources sometimes it is easier to find out the voltage across or current in a
branch of the circuit by considering the effect of one source at a
time by replacing the other
sources with their ideal internal resistances.
Superposition Theorem Statement:
Any linear, bilateral two terminal network consisting
of more than one sources,
The total current or voltage in any part of a network is equal to the algebraic sum of the currents
or voltages in the required branch with each source acting individually
while other sources are
replaced by their ideal internal resistances. (i.e. Voltage sources by
a short circuit and current
sources by open circuit)
