When an R-L-C circuit is resonant, what is true about the total impedance?

When an R-L-C circuit is resonant, what is true about the total impedance?

• A. It is zero
• B. It is maximum
• C. It is minimum
• D. It fluctuates

Answer: (C)

In an R-L-C circuit (which includes a resistor, an inductor, and a capacitor), resonance occurs at a specific frequency where the inductive reactance and capacitive reactance are equal in magnitude but opposite in phase. This leads to them canceling each other out. At this resonant frequency, the impedance of the circuit is determined solely by the resistance (R) in the circuit. The total impedance (Z) at resonance can be expressed as Z = R, where the reactance (X_L - X_C) becomes zero. Since the impedance comprises resistance and reactance, being at resonance means that the reactance does not contribute to the total impedance, resulting in the minimum possible impedance for the circuit. This unique condition allows for maximum current flow in the circuit for a given voltage, as the opposition to current is minimized. Therefore, the notion that the total impedance is at its minimum at resonance is accurate. The other options do not capture this specific relationship of impedance at the resonant frequency in an R-L-C circuit.

In an R-L-C circuit (which includes a resistor, an inductor, and a capacitor), resonance occurs at a specific frequency where the inductive reactance and capacitive reactance are equal in magnitude but opposite in phase. This leads to them canceling each other out.

At this resonant frequency, the impedance of the circuit is determined solely by the resistance (R) in the circuit. The total impedance (Z) at resonance can be expressed as Z = R, where the reactance (X_L - X_C) becomes zero. Since the impedance comprises resistance and reactance, being at resonance means that the reactance does not contribute to the total impedance, resulting in the minimum possible impedance for the circuit.

This unique condition allows for maximum current flow in the circuit for a given voltage, as the opposition to current is minimized. Therefore, the notion that the total impedance is at its minimum at resonance is accurate. The other options do not capture this specific relationship of impedance at the resonant frequency in an R-L-C circuit.