Sunday, 16 December 2012

Solved Problem Based On Maximum Power Transfer Theorem

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

For the above network, we are going to find-out the value of unknown resistance called “RL”. 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 RL. 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 Vo.c.
Here, Vo.c is known as voltage between open circuits.
So, steps are:-
For this circuit using Mesh-analysis. We get
Applying Kvl in loop 1st:-
6-6I1-8I1+8I2=0
-14I1+8I2=-6         ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ (1)
Again, Applying Kvl in loop 2nd:-
-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 Vo.c is
VA-5I2- VB = 0
Vo.c/ VAB= 5I2 = 5X0.167 = 0.835v
So, the maximum power through the RL is given by:-