Power of an electrical circuit is equal to current squared times resistance.(adsbygoogle = window.adsbygoogle || []).push({});

My expression for current is: E/(R + r), where E is emf of battery.

So, my expression for Power, P, is:

P=((E^2)R)/(R + r)^2

I would like to differentiate P with respect to R, to find where the slope is zero, ie., the maximum power.

I am having some trouble though. I used the quotient rule and got:

((R + r)E^2 - 2RE^2)/(R + r)^3

Is this correct? I need to know where this is zero, but I am a bit unsure about where to go from here.

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# Differentiation maximum problem

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