JAMB Physics 2023 Paper

Concept:In a series RLC circuit, the effective potential difference is the phasor sum of the resistor voltage and the resultant of the inductor and capacitor voltages.Explanation:From the diagram, the voltages are $V_R = 30\,V$, $V_L = 60\,V$, and $V_C = 120\,V$.Since $V_L$ and $V_C$ act in opposite directions, their resultant is $(V_L - V_C)$.The effective voltage is given by:$$V = \sqrt{V_R^2 + (V_L - V_C)^2}$$Substitute the values:$$V = \sqrt{30^2 + (60 - 120)^2}$$$$V = \sqrt{900 + (-60)^2}$$$$V = \sqrt{900 + 3600}$$$$V = \sqrt{4500}$$$$V \approx 67.08\,V$$So the effective potential difference is approximately $67\,V$.Answer:B. 67