Electrical circuits lecture notes b. Tech

Maximum Power Transfer Theorem Statement: 
Any linear, bilateral two terminal network consisting of a resistance load, being 
connected to a dc network, receives maximum power when the load resistance is equal to the 
internal resistance (Thevenin’s equivalent resistance) of the source network as seen from the load 
terminals. 
According to Maximum Power Transfer Theorem, for maximum power transfer from the 
network to the load resistance , 
R
L
must be equal to the source resistance i.e. Network’s 
Thevenin equivalent resistance 
R
Th
 . i.e. R
L
 = R
Th 

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The load current 
I
in the circuit shown above is given by,
𝐼 =
𝑉
𝑇𝐻
𝑅
𝑇𝐻
+𝑅
𝐿
The power delivered by the circuit to the load: 
𝑃 = 𝐼
2
𝑅 =
𝑉
𝑇𝐻
2
(𝑅
𝑇𝐻
+𝑅
𝐿
)
2
𝑅
𝐿
The condition for maximum power transfer can be obtained by differentiating the above 
expression for power delivered with respect to the load resistance (Since we want to find out the 
value of 
R
L
for maximum power transfer) and equating it to zero as : 
𝜕𝑃
𝜕𝑅
𝐿
= 0 =
𝑉
𝑇𝐻
2
(𝑅
𝑇𝐻
+𝑅
𝐿
)
2
−
2𝑉
𝑇𝐻
2
(𝑅
𝑇𝐻
+𝑅
𝐿
)
3
𝑅
𝐿
= 0
Simplifying the above equation, we get: 
(𝑅
𝑇𝐻
+ 𝑅
𝐿
) − 2𝑅
𝐿
= 0 ⟹
𝑅
𝐿
= 𝑅
𝑇𝐻
Under the condition of maximum power transfer, the power delivered to the load is given by : 
𝑃
𝑀𝐴𝑋
=
𝑉
𝑇𝐻
2
(𝑅
𝐿
+𝑅
𝐿
)
2
× 𝑅
𝐿
=
𝑉
𝑇𝐻
2
4𝑅
𝐿
Under the condition of maximum power transfer, the efficiency 
𝜼
of the network is then given 
by: 
𝑃
𝐿𝑂𝑆𝑆
=
𝑉
𝑇𝐻
2
(𝑅
𝐿
+𝑅
𝐿
)
2
× 𝑅
𝑇𝐻
=
𝑉
𝑇𝐻
2
4𝑅
𝐿
𝜼 =
output
input
=
𝑉
𝑇𝐻
2
4𝑅
𝐿
(
𝑉
𝑇𝐻
2
4𝑅
𝐿
+ 𝑉
𝑇𝐻
2
4𝑅
𝐿
)
= 0.50
For maximum power transfer the load resistance should be equal to the Thevenin equivalent 
resistance ( or Norton equivalent resistance) of the network to which it is connected . Under the 
condition of maximum power transfer the efficiency of the system is 50 %.