sorry for inturruption.....
In the above figure, I take Rs is variable and R(load) = 3ohms and Vs=20V then what is the value of Rs?
I want to give options also
options: A) 1 ohm B) 2 ohms C) 3 ohms D) 4 ohms
Your question is not an application of the Maximum Power Transfer Theorum. Maximum power will be delivered to the load when Rs=0 ohms.
An increase in Rs will cause a decrease in current and a decrease in load voltage. Hence load power will decrease.
The Maximum Power Transfer Theorum applies when the load resistance is matched to the fixed internal resistance of the voltage source.
Now, when load resistance increases, current still decrease but load voltage increases. At Rl=0, the load voltage and hence load power is zero.
At Rl=infinity, the load current and hence load power is zero.
In general, Pl = (Vs^2 * Rl)/(Rl + Rs)^2 for the given circuit.
As you can see, if Rl and Vs are held constant then Pl is a maximum when Rs is zero since Rs is only in the denominator.
However, Rl is a different story since it exists in both numerator and denominator.
If you differentiate this equation with respect to Rl and solve for d (Pl) / d (Rl) = 0 the solution for Rl>0 should be Rl=Rs