Physics - Current Electricity Question with Solution | TestHub

The current flowing through the circuit is $I=\frac{E}{R_{ext}+r}$. The power dissipated in the external resistor is $P=I^2{R}_{ext}={\left(\frac{E}{R_{ext}+r}\right)}^2{R}_{ext}$. To find the maximum power, we differentiate $P$ with respect to $R_{ext}$ and set it to zero, or simply apply the maximum power transfer theorem. According to this theorem, the power dissipated in the external resistor is maximum when the external resistance is equal to the internal resistance of the source, i.e., $R_{ext}=r$.