JAMB Physics 2023 Paper

Concept:Series resistances add up, while parallel resistances follow the reciprocal rule for equivalent resistance.Explanation:First, combine the two series resistors.$R_1 = 35\ \mathrm{k}\Omega + 40\ \mathrm{k}\Omega = 75\ \mathrm{k}\Omega$This $75\ \mathrm{k}\Omega$ is then connected in parallel with the unknown resistance $R$.The equivalent resistance of this parallel combination is given as $25\ \mathrm{k}\Omega$.Using the parallel formula:$$\frac{1}{R_{\text{eq}}} = \frac{1}{R} + \frac{1}{R_1}$$Substitute the known values:$$\frac{1}{25} = \frac{1}{R} + \frac{1}{75}$$Solve for $\frac{1}{R}$:$$\frac{1}{R} = \frac{1}{25} - \frac{1}{75}$$$$\frac{1}{R} = \frac{3 - 1}{75} = \frac{2}{75}$$Therefore:$$R = \frac{75}{2} = 37.5\ \mathrm{k}\Omega$$Answer:B. $37.5\ \mathrm{k}\Omega$