### Correct Option: B. The capacitive reactance is equal to the inductive reactance. #### Detailed Explanation: In a series RLC (Resistor, Inductor, Capacitor) circuit, resonance occurs when the inductive reactance (XL) and capacitive reactance (XC) are equal. This condition can be mathematically expressed as: \[ X_L = X_C \] Where: - \( X_L = \omega L \) (Inductive reactance) - \( X_C = \frac{1}{\omega C} \) (Capacitive reactance) - \( \omega = 2\pi f \) (Angular frequency, where \( f \) is the frequency of the AC source) At resonance, the circuit behaves in a very specific way: 1. The total impedance (Z) of the circuit is minimized and is purely resistive, meaning that the impedance is equal to the resistance (R) of the circuit. 2. The voltage across the inductor (V_L) and the capacitor (V_C) can become significantly larger than the source voltage (V_s) due to the phenomenon of resonance, where the energy oscillates between the inductor and capacitor. **Why Option B is Correct:** - When \( X_L = X_C \), the net reactance in the circuit becomes zero. This means that the total impedance is purely resistive (Z = R), allowing maximum current to flow through the circuit. Since the voltage across the inductor and capacitor can be much higher than the source voltage due to the phase relationship, this condition leads to maximum voltage across both components. #### Why the Other Options are Incorrect: **A. The inductive reactance is equal to the resistive impedance.** - This statement is incorrect because resonance is not defined by the equality of inductive reactance and resistive impedance. Instead, resonance specifically requires the equality of inductive and capacitive reactance. If \( X_L = R \), it does not guarantee resonance; it simply indicates a different condition in the circuit. **C. The total impedance is minimized.** - While it is true that at resonance the total impedance is minimized, this option is vague. The condition for resonance is specifically that \( X_L = X_C \). Simply stating that the total impedance is minimized does not capture the necessary condition for resonance, which is the equality of the reactances. **D. The resistance is zero.** - This option is misleading. While having zero resistance would minimize impedance, it does not lead to resonance. In practical circuits, resistance is always present, and resonance occurs at the point where the reactances are equal, regardless of the resistance value. Zero resistance would lead to an ideal scenario that does not reflect real-world applications. ### Summary of Key Points: - Resonance in a series RLC circuit occurs when the inductive reactance equals the capacitive reactance (\( X_L = X_C \)). - At resonance, the total impedance is minimized and is purely resistive, allowing maximum current flow. - The voltages across the inductor and capacitor can be significantly higher than the source voltage due to energy oscillation. - Understanding the specific conditions for resonance is crucial for analyzing RLC circuits effectively.