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 4
 Homework Statement
 The question is in Attempt at a solution
 Homework Equations

V=IR
P=V^2/R
P=I^2×R
My attempt:
So the resistance is coming to be negative.Can anyone tell me my mistake.Thanks.
Formally your answer is correct. Input source impedance is (36 Ohm)=2 Ohm, therefore from matching theorem your load must be also 2 Ohm for maximal transferred power. You just need to trim negative resistance answer to closest physical value (i.e. 0).Homework Statement: The question is in Attempt at a solution
Homework Equations: V=IR
P=V^2/R
P=I^2×R
View attachment 249522
My attempt:
View attachment 249523
So the resistance is coming to be negative.Can anyone tell me my mistake.Thanks.
Your error is in assuming all minima are local minima, i.e. where a gradient is zero.So the resistance is coming to be negative.Can anyone tell me my mistake.Thanks.
Can you please explain me how can i do that here means how can i find the range of R.Your error is in assuming all minima are local minima, i.e. where a gradient is zero.
Sometimes the global minimum occurs at one end of the valid range. In general, you should check the extremities of the range even if you do find a local minimum.
The range of R should either be given by the problem(for example in this problem it could have been given that the variable resistor is in the range for example ##[4,404]##) or can be logically inferred like for example in this problem the range of R is logically inferred to be ##[0,+\infty)##. So you look for maximum or minimum at the end points and how to prove that the value at the end point is a maximum (or minimum).Can you please explain me how can i do that here means how can i find the range of R.
You worked out the derivative. You looked for zeros. Good. Now check the value of the function and the derivative at the end points.As @trurle posted, it cannot be negative.