:Figure 8.7 shows how P is a function of Rand it has a maximum value P = ε^2/4r
This happens when R=r
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To explain this

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P is a function of I &V ; P= I×V
I is decresing as R increase at constant V
V is decreasing As R increase at constant I
So there is one value of R when they equal (thier carves are intersect) and this value is R=r ;
On other words ; at this value of R gives maximum of the product of V with I which is Pmax [/