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Thevenin’s Theorem
Statement: Thevenin’s Theorem states that “Any two terminal linear circuit containing a large number of voltage and/or current sources and resistors can be replaced by a simple equivalent circuit containing a single voltage source and a series resistor”.
Thevenin’s Equivalent Circuit
Here, Vth = Voc (open-circuit voltage) Rth = equivalent R (total R) in the circuitRL = load resistance of the network through which the current or across which the voltage is to be calculated
Now, Current through RL = Vth / (Rth+RL)
3Ω
2Ω
10V
10Ω
RL
2Ω
Steps to solve circuit using Thevenin’s Theorem Calculation of VTH :
1. Remove the component of interest - normally called the load resistance(RL).
2. Mark the terminals as VTH where the load was removed from.
3. Calculate the Thevenin Voltage VTH by finding the open circuit voltage across the load terminals - remember that no current flows into an open circuit
Calculation of RTH :1. Calculate the Thevenin Resistance RTH by
a. Marking the terminals as RTH where the load was removed from and setting all sources to zero (voltage sources are replaced by a short circuit and current sources by an open circuit)
b. Finding the resistance between the two load terminals.
2. Draw the Thevenin equivalent circuit and return the load for analysis.
Example
3Ω
2Ω
10V
10Ω
RL
2Ω
Find Thevenin’s equivalent circuit and the current passing through RL given RL = 1Ω
3Ω
2Ω
10V
10Ω
2Ω
VXV
Ai
TH 623
25/10
Step 1: Remove RL and mark points A and B Step 2: Find VTH
A
B
i
3Ω
2Ω
10V
10Ω
2Ω
3Ω
2Ω 10Ω
2Ω
To find RTh Short Circuit voltage source
RTH
2.13
10]32
322[
10]]3||2[2[THR
Step 3: Find RTH
13.2Ω
6V RL
Thevenin’s equivalent circuit
The current through RL = 1Ω is A423.012.13
6
Example
3Ω
2Ω 10Ω
RL
2Ω
1A
Example: Find Thevenin’s equivalent circuit
Step 1:Remove RLStep2: Find VTH
3Ω
2Ω 10Ω
2Ω
1A
VVTH 331
3Ω
2Ω 10Ω
2Ω
Open circuit current source
RTH
15
2310THR
Step 3: Find RTH
3Ω
2Ω 10Ω
2Ω
1A
15Ω
3V RL
Step4: Thevenin’s equivalent circuit
R3=4K
R2=8K
R1=2K
R4=2K
RL=1K10V
+ -
Example:Find Thevenin’s equivalent circuit across RL
Step 1: Remove RLStep 2: Find VTH
R3=4K
R2=8K
R1=2K
R4=1K
10V
0V
10V
8V 2V
Here,I1=10/10=1AI2=10/5=2A
I1 I2
+ -VTH
Now, VTH - 2I - 4I = 0or VTH - 2 ( -I1 ) – 4 (I2) = 0Or VTH = 8 – 2 = 6V
Step 3:Find RTH
R3=4K
R2=8K
R1=2K
R4=1K
RTH
R3=4K
R2=8K
R1=2K
R4=1K
R3=4K
R2=8K
R1=2K
R4=1K
A B
C
D
A B
C
D
C
D
A B
R3=4K
R2=8K
R1=2K
R4=1K
KKK
KKKKRTH4.28.06.1
1||48||2
2.4K
6V RL
Step 4:Thevenin’s equivalent circuit
For the circuit below, find VAB usingThevenin Theorem .
+_2 0 V
5
2 0
1 0
1 7
1 .5 A
A
B
We first find VTH with the 17 resistor removed.Next we find RTH by looking into terminals A-Bwith the sources deactivated.
Example
VTHVth
I Vth
I
15V
31VVth 1,in Putting
0.8
20/25 I Also
.....1..........20I.......15Vthor
020I-15-
Vth
5(20)10 14
(5 20)THR
RthRTH
1 4
3 1 VV TH
R TH
1 7 V A B
+
_
+_
A
B
Thevenin’s equivalent circuit is
We can easily find that,
17ABV V
THEVENIN’S THEOREM: Example 10.4: Working with a mix of independent and dependent sources.
Find the voltage across the 100 load resistor by first findingthe Thevenin circuit to the left of terminals A-B.
+_ 8 6 V
5 0
3 0
4 0
1 0 0
6 IS
IS
A
B
VTH
Here, VTH = 30 Is + 6 Is
Also,
Calculate the Thevenin’s equivalent circuit seen by load RL
Example
VTH
I
7V- Vth 1,in putting
0.2 I ..
010I-55I-8 Also
....1..........8.........-5IVthor
05I-8Vth- Here,
ei
Rth
33.3
5 11 10
Rth
Therefore Thevenin’s equivalent circuit is
7V
3.33