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. $R=2r$
• B. $R=1000r$
• C. $R=r$
• D. $R=0.001r$

Answer 1

The correct option is C $R=r$


The current drawn in the circuit,

$i=\left(\frac{E}{R+r}\right)$

Power delivered to $R$ is,

$P=i^{2}R={\left(\frac{E}{R+r}\right)}^{2}R$

$P$ to be maximum, $\frac{dP}{dR}=0$

$\frac{d}{dR}\left[{\left(\frac{E}{R+r}\right)}^{2}R\right]=0$

$\Rightarrow R=r$

Hence, $\left(D\right)$ is the correct answer.