### Correct Option: C. 0° ### Detailed Explanation: In an alternating current (AC) circuit, resonance occurs when the inductive reactance (XL) and capacitive reactance (XC) are equal. This condition leads to a specific behavior in the circuit, particularly concerning the phase angle between the voltage and the current. 1. **Understanding Reactance**: - **Inductive Reactance (XL)**: This is the opposition to the change in current caused by an inductor and is given by the formula: \[ X_L = 2\pi f L \] where \( f \) is the frequency of the AC source and \( L \) is the inductance. - **Capacitive Reactance (XC)**: This is the opposition to the change in voltage caused by a capacitor and is given by the formula: \[ X_C = \frac{1}{2\pi f C} \] where \( C \) is the capacitance. 2. **Condition for Resonance**: - At resonance, the inductive reactance equals the capacitive reactance: \[ X_L = X_C \] - This means that the total reactance in the circuit is zero, and the circuit behaves purely resistively. 3. **Phase Angle**: - The phase angle (\(\phi\)) in an AC circuit is defined as the angle by which the current either leads or lags the voltage. It is determined by the relationship between the total impedance (Z) and the resistance (R) in the circuit. - The phase angle can be calculated using: \[ \tan(\phi) = \frac{X}{R} \] where \( X \) is the total reactance (which is zero at resonance). - Since \( X = 0 \) at resonance, we have: \[ \tan(\phi) = \frac{0}{R} = 0 \] - Therefore, the phase angle \(\phi\) is: \[ \phi = 0° \] ### Why Other Options Are Incorrect: - **Option A: 90°**: - A phase angle of 90° occurs in a purely inductive circuit where the current lags the voltage by 90°. This is not the case at resonance, where the circuit is purely resistive. - **Option B: 60°**: - A phase angle of 60° does not correspond to any specific condition in a standard RLC circuit. It suggests a combination of resistive and reactive components but does not represent resonance. - **Option D: 180°**: - A phase angle of 180° indicates that the current is completely out of phase with the voltage, which is characteristic of a purely resistive load with negative impedance. This does not occur at resonance. ### Summary of Key Points: - At resonance in an AC circuit, inductive and capacitive reactances are equal, resulting in zero total reactance. - The phase angle between voltage and current is 0°, indicating that they are in phase. - Resonance leads to maximum current flow in the circuit, as impedance is minimized. - Understanding the relationship between reactance and phase angle is crucial for analyzing AC circuits. This thorough understanding of resonance and phase angles will help you tackle related questions in your physics exams effectively!