Question 282: Current Electricity

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 :-

Accepted Answer

Current i = $${E \over {r + R}}$$
Power generated in R
P = i
2
R
$$P = {{{E^2}R} \over {{{\left( {r + R} ight)}^2}}}$$
For maximum power $${{dP} \over {dR}} = 0$$
$${E^2}\left[ {{{{{\left( {r + R} ight)}^2} 	imes 1 - R 	imes 2(r + R)} \over {{{\left( {r + R} ight)}^4}}}} ight] = 0$$
$$ \Rightarrow $$ r = R or R = r

Answer

R = 1000 r

Answer

R = r

Answer

R = 2r

Answer

R = 0.001 r

Current Electricity

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 :-

Choose the correct answer: