Maximum Power Transfer Theorem Proof

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The maximum power transfer theorem states that maximum power will be delivered to the load resistance when the load resistance is equal to the thevenin's equivalent resistance of the circuit. If the load resistance is less or more than the thevenin's equivalent resistance, then power delivered to the load is less than the maximum.


Maximum power transfer theorem derivation



Derivation for maximum power transfer theorem is derived below:

Let the load current is given by the expression:


 Than power delivered to load is given by:
The power will be maximum when we differentiate power with respect to R and put equal to 0


On solving it further:


On solving further:



RTH2VOC2 = RL2VOC2



Value of Maximum Power is given by:




 

Hence maximum power delivered to the load is 50%. Even the load resistance is equal to the thevenins equivalent resistance, maximum power is only 50%. If the load resistance value is less or more than thevenins resistance then the power delivered will be less than 50 %.
 
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