- #1

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## Homework Statement

My physics teacher (i'm in year 12) set me a "challenge" to prove a graph in our textbook, which shows Power against Resistance, with a local maximum where

*R*= internal resistance,

*r*. He told me i'd need to use differentiation,

*P = I[tex]^{2}[/tex].R*

and said that I was right in thinking that I had to do something to do with there being a stationary point at

*R = r*, but in all honesty I am pretty stumped at where to start.

## Homework Equations

*P = I[tex]^{2}[/tex].R*

P = [tex]\frac{V^{2}}{R}[/tex]

P = [tex]\frac{V^{2}}{R}[/tex]

## The Attempt at a Solution

Well all i've really said so far is that,

[tex]\frac{dP}{dR}[/tex] = I[tex]^{2}[/tex]

and that at

*R = r*, [tex]\frac{dP}{dR}[/tex] = 0, so

*I*= 0.

The problem is... I don't really understand what I am trying to prove, is it simple enough to just say that max power is dissipated when

*I = 0*, and

*I = 0*when

*R = r*, or am I skimming over some deeper truth?

Any help would be appreciated, but i'd prefer guidance instead of a full answer :)