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Question

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

A
R=2 r
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B
R=1000 r
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C
R=r
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D
R=0.001 r
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Solution

The correct option is C R=r

The current drawn in the circuit,

i=(ER+r)

Power delivered to R is,

P=i2R=(ER+r)2R

P to be maximum, dPdR=0

ddR[(ER+r)2R]=0

R=r

Hence, (D) is the correct answer.

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