In a series RLC circuit, the total impedance is minimum when _______.

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  1. XL < Xc
  2. XL > Xc
  3. the resistance is zero
  4. XL=XC

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Option 4 : XL=XC
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Series Resonance

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A series RLC circuit exhibits resonance when the inductive and capacitive reactances are equal in magnitude but opposite in phase, resulting in a purely resistive impedance, and the value of impedance is minimum.

The impedance of the series RLC circuit is given by:

\(Z=\sqrt{R^2+(X_L^2-X_C^2)}\)

At X= XC

\(Z=\sqrt{R^2+(X_L^2-X_L^2)}\)

Z = R 

The impedance value is minimum.

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