**Correct Option: B. The impedance is purely resistive.** ### Detailed Explanation: In a series RLC (Resistor, Inductor, Capacitor) circuit, resonance occurs at a specific frequency known as the resonant frequency. At this frequency, the inductive reactance (XL) and capacitive reactance (XC) are equal in magnitude but opposite in phase. This means that they cancel each other out. 1. **Understanding Impedance in RLC Circuits:** - The total impedance (Z) in a series RLC circuit is given by the formula: \[ Z = R + j(X_L - X_C) \] where: - \( R \) is the resistance, - \( X_L = \omega L \) is the inductive reactance, - \( X_C = \frac{1}{\omega C} \) is the capacitive reactance, - \( j \) is the imaginary unit. 2. **At Resonance:** - At resonance, the condition \( X_L = X_C \) holds true. Therefore, the equation simplifies to: \[ Z = R + j(0) = R \] - This means that the impedance is purely resistive, with no imaginary component (reactance) present. The circuit behaves like a simple resistor. 3. **Implications of Purely Resistive Impedance:** - When the impedance is purely resistive, the circuit allows maximum current to flow at the resonant frequency. This is because the total impedance is minimized (equal to R), and the phase angle between the voltage and current is zero, indicating that they are in phase. ### Why Other Options Are Incorrect: - **Option A: The impedance is at its maximum value.** - This statement is incorrect because, at resonance, the impedance is minimized (equal to the resistance \( R \)). The maximum impedance would occur at frequencies far from resonance, where either the inductive or capacitive reactance dominates. - **Option C: The impedance is zero.** - This is also incorrect. While the impedance at resonance is minimized to \( R \), it is not zero unless the resistance itself is zero, which is not a practical scenario in real circuits. A zero impedance would imply an ideal short circuit, which is not the case here. - **Option D: The impedance is equal to the inductive reactance.** - This statement is incorrect because, at resonance, the inductive reactance \( X_L \) and capacitive reactance \( X_C \) cancel each other out. Therefore, the impedance is not equal to the inductive reactance; it is simply equal to the resistance \( R \). ### Summary of Key Points: - At resonance in a series RLC circuit, the inductive and capacitive reactances cancel each other out. - The total impedance becomes purely resistive, equal to the resistance \( R \). - This results in maximum current flow at the resonant frequency, with voltage and current in phase. - Understanding resonance is crucial for analyzing RLC circuits and their behavior in AC applications. This thorough understanding of resonance and impedance in RLC circuits is essential for mastering the concepts in physics related to alternating current circuits.