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1. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 1
Thevenin’s Theorem
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2. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 2
Thevenin’s Theorem
 It was first proposed by a French telegraph
engineer, M.L. Thevenin in 1883.
 There also exists an earlier statement of the
theorem credited to Helmholtz.
 Hence it is also known as Helmholtz-Thevenin
Theorem.
 It is useful when we wish to find the response
only in a single resistance in a big network.
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3. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 3
Thevenin’s Theorem
 Any two terminals AB of a network
composed of linear passive and active
elements may by replaced by a simple
equivalent circuit consisting of
1. an equivalent voltage source Voc, and
2. an equivalent resistance Rth in series.
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4. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 4
 The voltage Voc is equal to the potential
difference between the two terminals AB caused
by the active network with no external
resistance connected to these terminals.
 The series resistance Rth is the equivalent
resistance looking back into the network at the
terminals AB with all the sources within the
network made inactive, or dead.
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5. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 5
Illustrative Example 3
 Using Thevenin’s theorem, find the current in
resistor R2 of 2 Ω.
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6. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 6
Solution :
1. Designate the resistor R2 as “load”.
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7. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 7
2. Pull out the load resistor and enclose the remaining
network within a dotted box.
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8. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 8
3. Temporarily remove the load resistor R2, leaving the
terminals A and B open .
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9. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 9
4. Find the open-circuit voltage across the terminals A-
B,
V
11.2









1
2
.
4
7
A;
4.2
5
21
1
4
7
28
AB
V
I
5. This is called Thevenin voltage, VTh = VAB = 11.2 V.
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10. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 10
6. Turn OFF all the sources in the circuit
Find the resistance between terminals A and B. This is
the Thevenin resistance, RTh. Thus,
1 4
1 || 4
1 4
Th
R

    

0.8 Ω
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11. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 11
7. The circuit within the dotted box is replaced by the
Thevenin’s equivalent, consisting of a voltage source of
VTh in series with a resistor RTh,
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12. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 12
8. The load resistor R2 is again connected to Thevenin’s
equivalent forming a single-loop circuit.
• The current I2 through this resistor is easily calculated,
Th
2
Th 2
11.2
0.8 2
V
I
R R
  
 
4 A
Important Comment
The equivalent circuit replaces the circuit within the
box only for the effects external to the box.
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13. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 13
Example 4
 Using Thevenin’s Theorem, find the current in the
ammeter A of resistance 1.5 Ω connected in an
unbalanced Wheatstone bridge shown.
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14. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 14
Solution :
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15. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 15
V
6
















6
5
.
1
4
75
.
0
A
5
.
1
6
2
12
and
A
75
.
0
4
12
12
2
1
BD
AD
AB
oc V
V
V
V
I
I
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16. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 16
Ans. -1 A
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17. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 17
Benchmark Example 5
Again consider our benchmark example to determine
voltage across 3-Ω resistor by applying Thevenin’s
theorem.
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18. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 18
Solution :
• We treat the 3-Ω resistor as load.
• Thevenin voltage VTh is the open-circuit voltage
(with RL removed).
• We use source transformation.
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19. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 19
V
5



 1
5
Th
V
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20. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 20
To compute RTh, we turn off all the sources in the
circuit within box and get the circuit
Thus, RTh = 3 Ω.
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21. शनिवार, 15 अप्रैल 2023 Ch. 4 Network Theorems 21
V
2.5




3
3
3
5
L
V
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