### Maximum Power Transfer Theorem Proof

Searching the books for your studies can be so easy
You can search in the search bar for your book .........................................................................

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: $\dpi{150} \fn_cm I=\frac{V_{OC}}{R_{TH}+R_{L}}= \frac{V_{OC}}{2R_{L}}$  $\dpi{150} \fn_cm P_{L Max}=I_{L}^{2}R_{L}= \left [ \frac{V_{OC}}{2R_{L}} \right ]^{2}\times R_{L}$

$\dpi{150} \fn_cm P_{L Max}=\frac{V_{OC}^{2}}{4R_{L}}$

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 %.