question_answer

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 :-             [JEE Main 8-4-2019 Afternoon]

A) R = 1000 r                 

B) R = 0.001 r

C) R = 2r            

D)   R = r

Correct Answer: D

Solution :

Current \[i=\frac{E}{r+R}\] Power generated in R \[P={{i}^{2}}R\] \[P=\frac{{{E}^{2}}R}{{{(r+R)}^{2}}}\] for maximum power\[\frac{dP}{dR}=0\] \[{{E}^{2}}\left[ \frac{{{\left( r+R \right)}^{2}}\times 1-R\times 2\left( r+R \right)}{{{\left( r+R \right)}^{4}}} \right]=0\]\[\Rightarrow r=R\]