### Correct Option: A. When the inductive reactance equals the capacitive 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 expressed mathematically as: \[ X_L = X_C \] Where: - \( X_L = 2\pi f L \) (Inductive reactance) - \( X_C = \frac{1}{2\pi f C} \) (Capacitive reactance) - \( f \) is the frequency of the applied AC voltage, - \( L \) is the inductance, - \( C \) is the capacitance. At resonance, the total impedance (Z) of the circuit is minimized, and it is purely resistive. The formula for the total impedance in a series RLC circuit is: \[ Z = R + j(X_L - X_C) \] Where \( j \) is the imaginary unit. At resonance, since \( X_L = X_C \), the imaginary part becomes zero, and the impedance simplifies to: \[ Z = R \] This means that the circuit behaves like a purely resistive circuit, allowing maximum current to flow through it, as per Ohm's law: \[ I = \frac{V}{Z} \] Where \( I \) is the current, \( V \) is the voltage, and \( Z \) is the impedance. Since \( Z = R \) at resonance, the current is maximized when the voltage is applied. ### Why Other Options Are Incorrect: **B. When the total resistance is minimized** - While minimizing resistance can help increase current, it is not the condition for resonance. Resonance specifically depends on the relationship between inductive and capacitive reactance, not just the resistance. A circuit can have low resistance but not be at resonance if \( X_L \) and \( X_C \) are not equal. **C. When the applied voltage is at its peak** - The peak voltage does not guarantee resonance. The condition for maximum current flow is not just about the voltage level but about the reactances being equal. The peak voltage can occur at any point in the AC cycle, regardless of whether the circuit is at resonance. **D. When the frequency is below the resonant frequency** - At frequencies below the resonant frequency, the inductive reactance is less than the capacitive reactance (\( X_L < X_C \)). This condition does not lead to maximum current flow; instead, the circuit behaves differently, and the current is not maximized. Resonance occurs at a specific frequency where \( X_L = X_C \). ### Summary of Key Points: - Resonance in a series RLC circuit occurs when inductive reactance equals capacitive reactance (\( X_L = X_C \)). - At resonance, the total impedance is minimized to just the resistance \( R \), allowing maximum current flow. - Other conditions, such as minimizing resistance or having peak voltage, do not define resonance. - Frequencies below the resonant frequency do not maximize current flow, as the reactances are not balanced. This understanding of resonance is crucial for analyzing and designing circuits in various applications, including radio transmitters, audio equipment, and other electronic devices.