RRB Technician Grade I 19 Dec 2024 Shift 3 Paper

Concept:In a series circuit, the total resistance is the sum of individual resistances, and the same current flows through all components. The voltage across any resistor is found using Ohm's law.Explanation:Given: $R_{1} = 10\ \Omega$, $R_{2} = 20\ \Omega$, and battery voltage $V = 12\ \text{V}$.Since the resistors are in series, the total resistance is:$$R_{\text{total}} = R_{1} + R_{2} = 10\ \Omega + 20\ \Omega = 30\ \Omega.$$Now, find the current in the circuit using Ohm's law:$$I = \frac{V}{R_{\text{total}}} = \frac{12\ \text{V}}{30\ \Omega} = 0.4\ \text{A}.$$This current flows through both resistors equally because they are in series.To find the voltage across $R_{2}$, apply Ohm's law again:$$V_{R_2} = I \times R_{2} = 0.4\ \text{A} \times 20\ \Omega = 8\ \text{V}.$$Therefore, the voltage across $R_{2}$ is $8\ \text{V}$, which corresponds to option C.Answer:$8\ \text{V}$ (Option C)