For an LCR circuit [y axis represent either Z, R,  $X_L,X_C$]

LCR Circuit Impedance and Reactance

Impedance and Reactance in an LCR Circuit

For an LCR series circuit, the impedance Z is given by:

Z = √R² + (X_C - X_L)²

Where reactances are:

• Inductive reactance: X_L = ωL
• Capacitive reactance: X_C = 1 / (ω C)

At resonance frequency ω = ω^’, we have X_L = X_C which leads to Z = R.

Hence, the phase difference between current and voltage is zero at resonance.

Y-Axis Representation

The Y-axis of a graph related to an LCR circuit versus frequency may represent:

• Impedance (Z)
• Resistance (R) - usually a constant horizontal line
• Inductive Reactance (X_L) - increases linearly with frequency
• Capacitive Reactance (X_C) - decreases with increasing frequency

This is important for understanding the frequency response and resonance behavior of the circuit.