The discussion revolves around a resistor circuit problem related to maximum power transfer and the implications of negative resistance values. Participants are exploring the conditions under which resistance can be defined and the mathematical reasoning behind determining maxima and minima in this context.
Some participants have provided guidance on checking the endpoints of the resistance range and the implications of the derivative at those points. There is an ongoing exploration of the assumptions made regarding the resistance values and the conditions for maximum power transfer.
Participants note that the range of resistance values is not explicitly provided in the problem statement, leading to discussions on logical inference of the range and the physical constraints on resistance values.
Formally your answer is correct. Input source impedance is (3||6 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).Physics lover said:
Your error is in assuming all minima are local minima, i.e. where a gradient is zero.Physics lover said:
Can you please explain me how can i do that here means how can i find the range of R.haruspex said:
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).Physics lover said:
haruspex said: