**Correct Option: B. The impedance is equal to the resistance only.** ### Detailed Explanation: In a series RLC circuit, resonance occurs when the inductive reactance (XL) and capacitive reactance (XC) are equal in magnitude but opposite in phase. This condition can be expressed mathematically 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) At resonance, the total impedance (Z) of the circuit can be calculated using the formula: \[ Z = R + j(X_L - X_C) \] Where: - \( R \) is the resistance, - \( j \) is the imaginary unit, - \( X_L \) is the inductive reactance, - \( X_C \) is the capacitive reactance. Since \( X_L = X_C \) at resonance, the equation simplifies to: \[ Z = R + j(0) = R \] This means that the impedance of the circuit at resonance is purely resistive and equal to the resistance \( R \) of the circuit. There is no reactive component (inductive or capacitive) contributing to the impedance at this point. ### Why the Other Options are Wrong: **A. The impedance is equal to zero.** - This statement is incorrect because while the reactive components cancel each other out at resonance, the impedance is not zero. The circuit still has resistance \( R \), which contributes to the total impedance. Therefore, the impedance cannot be zero. **C. The impedance is equal to the inductive reactance.** - This option is incorrect because at resonance, the inductive reactance \( X_L \) is canceled out by the capacitive reactance \( X_C \). Thus, the impedance is not equal to the inductive reactance; it is simply equal to the resistance \( R \). **D. The impedance is equal to the capacitive reactance.** - Similar to option C, this statement is also incorrect. At resonance, the capacitive reactance \( X_C \) is canceled out by the inductive reactance \( X_L \). Therefore, the impedance cannot be equal to the capacitive reactance; it is equal to the resistance \( R \). ### Summary of Key Points: - At resonance in a series RLC circuit, the inductive and capacitive reactances are equal and cancel each other out. - The total impedance at resonance is purely resistive and equal to the resistance \( R \) of the circuit. - The correct answer is option B: the impedance is equal to the resistance only. - Understanding resonance is crucial for analyzing RLC circuits and their behavior in AC systems.