physics- electricity help

[cashem'up]

why is the power dissipated max when the internal resistance is equal to the load resistance................plz explain

[astarmathsandphysics]

It is a complicated maths thing. You differentiate and set equal to zero.

[cashem'up]

its ok can u show me how to do it......is it like finding the stationary point and the maxima and minima...........jst explain....nd then please support with theological statement

[astarmathsandphysics]

Ok when I get home

[astarmathsandphysics]

Pout=Iout Vout =V/(R+r)*VR/(R+r)=VR/(R+r)^2
d(P out)/dR =V((R+r)^2 -2(R+r)R)/(R+r)^4 =0
0=(R+r)^2-2(R+r)R
r^2-R^2=0 so r=R

[7ooD]

do they ask such question in edexcel as

[vanibharutham]

i have attached my method

its a bit different from astar's method, but works out to be the same i.e. R = r

[cashem'up]

thanks........yea that does make sense mathemetically but how would u explain it theoritacally....... i mean wat is actually happening

[astarmathsandphysics]

Thats what I meant by it being a mathematical answer. Because p=vi you have to maximise v and I but you cant do both and must use maths to do it.