RLC Series Circuit - Impedance at Resonance

At resonance, an RLC series circuit exhibits a unique behavior in terms of its impedance. The impedance, denoted by Z, represents the overall opposition to the flow of alternating current (AC) in a circuit. It is a complex quantity that includes both resistance (R) and reactance (X), where reactance can be inductive (XL) or capacitive (XC).

Impedance in an RLC Series Circuit
In an RLC series circuit, the impedance is given by the following expression:

Z = √(R^2 + (Xl - Xc)^2)

Where,
R = Resistance
Xl = Inductive reactance
Xc = Capacitive reactance

Impedance at Resonance
Resonance occurs in an RLC series circuit when the inductive reactance (Xl) is equal to the capacitive reactance (Xc). This can be expressed as:

Xl = Xc

At resonance, the impedance equation simplifies to:

Z = √(R^2)

Since the square root of a positive number is always positive, the impedance at resonance can be simplified as:

Z = R

Explanation
At resonance, the inductive and capacitive reactances cancel each other out, leaving only the resistance as the overall impedance. This means that at resonance, the impedance is purely resistive and its value is equal to the resistance of the circuit.

Interpretation
The impedance at resonance is minimum because it is purely resistive. This implies that there is no reactance to oppose the flow of current, resulting in a maximum current flow through the circuit. Therefore, the impedance at resonance is minimum, maximizing the circuit's ability to conduct current.

Summary
In an RLC series circuit, the impedance at resonance is minimum. This occurs when the inductive and capacitive reactances cancel each other out, leaving only the resistance as the overall impedance. At resonance, the impedance is purely resistive and its value is equal to the resistance of the circuit. This minimal impedance allows for maximum current flow in the circuit.