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