# THEVENIN`S and NORTON`S THEOREMS

```THEVENIN’S and NORTON’S
THEOREMS
Thevenin’s Theorem
Any linear one‐port circuit which contains resistors and
sources can be represented by an equivalent practical
voltage source consisting of an ideal voltage source Voc
which is the open‐ circuit voltage across the part,in
series with an equivalent resistance RTh,which is the
input resistant with independent sources killed.
Norton’s Theorem
Any linear one‐port circuit which contains resistors and
sources can be represented by an equivalent practical
current source consisting of an ideal current source Isc
which is the short‐ circuit current through the part,in
parallel with an equivalent resistance RTh,which is the
input resistant with independent sources killed.
Example
20
Voc 
.6  12V
46
4.6
RTh  1.6 
 4
46
If a load resistance of RL =6Ω is connected between A 12
and B :
 1 .2 A
IL 
46
VL  1.2  6  7.2V
PL  1.2  7.2  8.64W
If RL is changed to 20
12
IL 
 0.5 A
4  20
VL  20  0.5  10V
PL  10  0.5  5W
Note : Repeated solutions of the circuit for different loads are
very easy now.
Example
VK  Vx  Voc
VK  20 Vx
 0
4
10
10VK  200  4VK  0  VK 
20
 4A
4 1
100
Voc
3  25 
RTh 

isc
4
3
isc 
100
V  Voc
3
Example
Vx Vx
 1  0
6 2
 Vx  3Vx  6  0
Vx  3V
3
RTh   3
1

Example
Vx  3Vx Vx
 1  0
4
6
 6Vx  2Vx  12  0
12
Vx    3V
4
RTh  3
Maximum Power Transfer
2

RLVs 2
Vs 


 Rs  RL 
Rs  RL 2
To maximize PL with respect to RL
PL  RLiL2   RL 
Rs  RL   2Rs  RL RL  0
dPL
 Vs 2
dRL
Rs  RL 4
2
Rs  RL Rs  RL  2 RL   0  RL  Rs
In this case
Vs
Vs 2
VS
, VL 
, PL 
iL 
2 RL
2
4 RL
while
Vs 2
Pvs 
2 RL
Hence the maximum power transfer to the load is 50% of the power generated by the source.
```