Why is resistor power maximum in parallel with same value?

[Tuppe]

Hello, I want to ask the explanation for this basic problem.

So I have 2 resistors in parallel(X and Y) and I want to maximize the power going through the resistor X, by choosing the resistance.

This can be achieved only by choosing the same resistance for X, than Y has.
Why is this so? I can prove this resoult with numerical values, but I cannot derive the general solution.

Thank you!

 

[Jony130]

Resistors can only dissipate power in form of heat. So P = I^2 * R or P = V^2*R. So I don't understand your problem.
So please show numerical example.

 

[Doug Huffman]

Write P=R I^2 for R as two resistors in parallel and solve for Rx to see that it equals Ry.

P=E^2 R^-1

 

[Tuppe]

Thanks for quick answers!

I've tried the problem using the basic formulas of P = I^2 * R and P = V^2*R, but I only end up with a mess.

I cannot see where the maximum power comes in. I'd think that you need to derivate the solution to get the maximum.

Write P=R I^2 for R as two resistors in parallel and solve for Rx to see that it equals Ry.

I will end up with:
Rx=(-PRy/(P-RyI^2)), where the I is the combined current and P is combined power going through the equivalent resistor. I don't see how can I continue with that.

And I still cannot see how that is indeed the maximum value and not just something else.

 

[phinds]

Your statement as written does not lead to the conclusion you state. If there are, as stated in the problem as you expressed it, no constraints other than that you want to maximize the power dissipated in one of two parallel resistors, given a fixed applied voltage, then you simply make the value of that resistor as close to zero as you can and you will get more and more power dissipation in that resistor as you lower its value. I assume there is some other constraint that you have left out.

 

[Jony130]

Your statement as written does not lead to the conclusion you state. If there are, as stated in the problem as you expressed it, no constraints other than that you want to maximize the power dissipated in one of two parallel resistors, given a fixed applied voltage, then you simply make the value of that resistor as close to zero as you can and you will get more and more power dissipation in that resistor as you lower its value. I assume there is some other constraint that you have left out.

Yes, exactly. I think that OP made a mistake, and in reality he wants to find the max power in this circuit.
http://en.wikipedia.org/wiki/Maximu...mizing_power_transfer_versus_power_efficiency

 

[Tuppe]

Yes, exactly. I think that OP made a mistake, and in reality he wants to find the max power in this circuit.
http://en.wikipedia.org/wiki/Maximu...mizing_power_transfer_versus_power_efficiency

Yes, exactly thank you!

I was using current source instead, so I had the resistors in parallel in equivalent circuit. I'd think that there's a solution in that configuration too, but this is fine for me.

 

[sophiecentaur]

If you have a current source feeding two parallel resistors then, choosing an infinite value for one of the resistors will mean that I²R power will be dissipated in the remaining resistor. This the a maximum. If the two resistors are Equal in value, the total Power dissipated will be I²R/2 and the power dissipated in one of them will be I²R/4. Etc. Etc.