MAXIMUM POWER TRANSFER THEOREM

Statement: The power transferred by a source to the load resistance in a network is  maximum when the load resistance is equal to the internal  resistance of the source.

NOW LET US SOLVE AN EXAMPLE

Ques.) Find the value of R_L for the given network below that the power is maximum? And also find the Max Power through load-resistance R_L by using maximum power transfer theorem?

Solution: -

For the above network, we are going to find-out the value of unknown resistance called “R_L”. In previous post, I already show that when power is maximum through load-resistance is equals to the equivalent resistance between two ends of load-resistance after removing.

So, for finding load-resistance R_L. We have to find-out the equivalent resistance like that for this circuit:-

Now, For finding Maximum Power through load-resistance we have to find-out the value of V_o.c.

Here, V_o.c is known as voltage between open circuits.

So, steps are:-

For this circuit using Mesh-analysis. We get

Applying Kvl in loop 1^st:-

6-6I₁-8I₁+8I₂=0

-14I₁+8I₂=-6         ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ (1)

Again, Applying Kvl in loop 2^nd:-

-8I₂-5I₂-12I₂+8I₁=0

8I₁-25I₂=0             ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ (2)

On solving,eqn (1) & eqn (2), We get

I₁ = 0.524 A

I₂ = 0.167 A

Now, From the circuit V_o.c is

V_A-5I₂- V_B = 0

V_o.c/ V_AB= 5I₂ = 5X0.167 = 0.835v

So, the maximum power through the R_L is given by:-