JAMB Physics 2017 Paper

Concept:The resistors are connected in parallel, so the total current is found using the effective parallel resistance and Ohm’s law.Explanation:From the circuit, the $8\ \Omega$, $12\ \Omega$, and $6\ \Omega$ resistors are in parallel across a $12\ \text{V}$ supply.For parallel resistors, the effective resistance $R_{\text{eff}}$ is given by:$$\frac{1}{R_{\text{eff}}} = \frac{1}{8} + \frac{1}{12} + \frac{1}{6}$$Using the lowest common denominator $24$:$$\frac{1}{R_{\text{eff}}} = \frac{3 + 2 + 4}{24} = \frac{9}{24} = \frac{3}{8}$$So, the effective resistance is:$$R_{\text{eff}} = \frac{8}{3}\ \Omega \approx 2.67\ \Omega$$Now apply Ohm’s law, $V = IR$, to find the total current:$$I = \frac{V}{R_{\text{eff}}} = \frac{12}{\frac{8}{3}} = 12 \times \frac{3}{8} = 4.5\ \text{A}$$Answer:The total current in the circuit is $4.5\ \text{A}$, which is option C.