Question

How do you find the optimum load resistance?

Answer 1

I'm looking to find the optimum load resistance, could someone talk me through how to do it?

Answer 2

optimum load resistance is Rl.... in this ques i have used maximum power theorem which states that P=Vthevin^2/Rthevenin

Answer 3

First you need to obtain the expression of the power in RL as a function of I, Rs and RL.
Second, get the partial derivative of the function versus RL and make it equal to 0. The solution is the expression of optimal RL for maximum power transfer

Answer 4

For this circuit, the optimum load resistance, RL = RP+2*RS

Answer 5

Now that @hema_a85 has given the answer, here is the way it is obtained:

The current in the load is given by:
\[I_L=I · R_p/(R_p+2·R_s+R_L)\]
Power in the load is:
\[P_L=I_L^2·R_L=I^2·R_p^2·R_L/(R_p+2·R_s+R_L)^2\]
The load that makes power maximum has to fulfill:
\[\delta P_L/\delta R_L=0\]
\[I^2·R_p^2·[(R_p+2·R_s+R_L)^2-2·(R_p+2·R_s+R_L)·R_L]/(R_p+2·R_s+R_L)^4=0\] and this condition is fulfilled when:
\[(R_p+2·R_s+R_L)[R_p+2·R_s+R_L-2·R_L]=0\]

We have two solutions here:\[R_p+2·R_s+R_L=0\rightarrow R_L=-(R_p+2·R_s)\] and \[R_p+2·R_s-R_L=0\rightarrow R_L=R_p+2·R_s\]

The first solution has to be discarded for RL cannot have a negative value, therefore:
\[R_L=R_p+2·R_s\]

Answer 6

note that where it says "...and this condition is fulfilled when..." the previous expression equals to zero (it has been truncated by the equation editor)