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A cell of emf epsilon and internal resis...

A cell of emf `epsilon` and internal resistance r is connected across a load resistance R
(i) Find the maximum power delivered at the load ?
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Text Solution

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(i) Current through the load `l = ( epsilon)/( R + r )`
Power deliver at the load `P = l^(2) R = ( epsilon^(2) R )/( (R+r)^(2))`
Power deliverd at load is maximum , when `(dP)/(dR) = 0`
Solving above equation `R = r`
`P _(max) = ( epsilon^(2) r)/((r+r)^(2))= ( epsilon^(2))/( 4r)`
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