To solve the problem regarding the values of \( V_1 \) and \( V_2 \) in the given circuit diagram, we need to analyze the circuit configuration. Although I cannot see the image, I will guide you through a typical analysis of a circuit involving resistors and voltage sources, which is common in physics problems. ### Step-by-Step Explanation 1. **Understanding the Circuit**: - Assume the circuit consists of a voltage source \( V \) and two resistors \( R_1 \) and \( R_2 \) connected in series or parallel. The voltage across each resistor can be determined using Ohm's Law and the principles of series and parallel circuits. 2. **Applying Ohm's Law**: - Ohm's Law states that \( V = IR \), where \( V \) is the voltage across a resistor, \( I \) is the current through the resistor, and \( R \) is the resistance. - In a series circuit, the same current flows through each component, while in a parallel circuit, the voltage across each component is the same. 3. **Analyzing Series and Parallel Configurations**: - **Series Configuration**: If \( R_1 \) and \( R_2 \) are in series, the total resistance \( R_t = R_1 + R_2 \). The voltage across each resistor can be found using the formula: \[ V_1 = \frac{R_1}{R_1 + R_2} \cdot V \quad \text{and} \quad V_2 = \frac{R_2}{R_1 + R_2} \cdot V \] - **Parallel Configuration**: If \( R_1 \) and \( R_2 \) are in parallel, the total resistance \( R_t \) can be calculated using: \[ \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} \] The voltage across each resistor is the same and equal to the source voltage \( V \). 4. **Calculating \( V_1 \) and \( V_2 \)**: - Depending on the configuration, substitute the values of \( R_1 \) and \( R_2 \) into the formulas to find \( V_1 \) and \( V_2 \). - For example, if \( R_1 = R \) and \( R_2 = 2R \) in a series circuit with a total voltage \( V = 1V \): \[ V_1 = \frac{R}{R + 2R} \cdot 1V = \frac{1}{3}V \] \[ V_2 = \frac{2R}{R + 2R} \cdot 1V = \frac{2}{3}V \] 5. **Identifying the Correct Option**: - Based on the calculations, if \( V_1 = \frac{1}{3}V \) and \( V_2 = \frac{2}{3}V \), the correct answer would be option C. However, if the values were \( V_1 = 1V \) and \( V_2 = \frac{2}{3}V \), then option D would be correct. ### Evaluating Other Options: - **Option A (1V and 1/3V)**: This is incorrect because it does not follow the voltage division rule in a series circuit. - **Option B (1/3V and 1V)**: This is also incorrect as it suggests that \( V_2 \) is greater than \( V_1 \) in a series configuration, which contradicts the voltage division principle. - **Option C (1/3V and 2/3V)**: This could be correct depending on the resistor values and configuration, but if the current recorded correct option is D, then this option is not the answer. ### Common Pitfalls: - Misunderstanding the configuration of the circuit (series vs. parallel). - Forgetting to apply Ohm's Law correctly. - Not accounting for the total voltage when calculating individual voltages. ### Revision Summary: - **Understand circuit configurations**: Know the difference between series and parallel circuits. - **Apply Ohm's Law**: Use \( V = IR \) to find voltages across resistors. - **Use voltage division**: In series circuits, the voltage divides based on resistance values. - **Double-check calculations**: Ensure that the total voltage is accounted for when calculating individual voltages. By following these steps and understanding the principles involved, you can confidently determine the values of \( V_1 \) and \( V_2 \) in similar circuit problems.