First slide

Electrical power

Question

A cell of internal resistance r drives a current through an external resistance R. The power delivered by the cell to the external resistance is maximum when

Moderate

A

R = r
B

R >>r
C

R << r
D

R = 2r

Solution

let E = e.m.f. of cell and r = its internal resistance. Current through the cell
$i = \frac{E}{R + r}$
P = Power delivered to .R
$= i^{2} R = \frac{E^{2} R}{(R + r)^{2}}$
Power delivered will be maximum, when
$\frac{dP}{dR} = E^{2} [\frac{1}{(R + r)^{2}} - \frac{2 R}{(R + r)^{3}}] = 0$
Solving, we get E = r

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