The maximum power delivered to the external resistor occurs when the external resistance (R) is equal to the internal resistance (ri) of the battery. In this case, the power delivered (Pmax) can be calculated using the formula:
\[ P_{\text{max}} = \frac{V_{\text{max}}^2}{4R} \]
where \( V_{\text{max}} \) is the maximum voltage of the battery.
Since the battery voltage is 12V and the internal resistance is 4 ohms, the maximum power can be calculated as:
\[ P_{\text{max}} = \frac{(12V)^2}{4 \times 4 \Omega} \]
Solving this expression will give you the maximum power that can be delivered to the resistor.
