JAMB Physics 2017 Paper

Concept:Efficiency of a cell is the fraction of total electrical energy that is delivered to the external load rather than wasted inside the cell.Explanation:The cell has an internal resistance $r = 2\Omega$ and is connected to an external load resistor of resistance $R = 6\Omega$.Some of the cell's energy is lost as heat in the internal resistance, so only the power dissipated in the external resistor is useful output.Since power is given by $P = I^2R$, the efficiency of the cell is:$$\text{Efficiency} = \frac{\text{useful power}}{\text{total power}} \times 100\%$$$$\text{Efficiency} = \frac{I^2R}{I^2(R+r)} \times 100\%$$The current $I$ cancels out, leaving:$$\text{Efficiency} = \frac{R}{R+r} \times 100\%$$Substituting $R = 6\Omega$ and $r = 2\Omega$:$$\text{Efficiency} = \frac{6}{6+2} \times 100\% = \frac{6}{8} \times 100\%$$$$= 0.75 \times 100\% = 75\%$$Answer:D. $75.0\%$