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 :
Correct Option: , 4
Solution:
(4) $i=\left(\frac{\varepsilon}{R+r}\right)$
Power delivered to $\mathrm{R}$.
$P=i^{2} R=\left(\frac{\varepsilon}{R+r}\right)^{2} R$
$\mathrm{P}$ to be maximum, $\frac{d P}{d R}=0$
or $\frac{d}{d R}\left[\left(\frac{\varepsilon}{R+r}\right)^{2} R\right]=0$
or $R=r$