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In a pure LC circuit that is left to oscillate at its natural frequency without any AC source, would there be any \$X_L\$ or \$X_C\$? I don't think there is any reactance in such a circuit, because there isn't any AC source driving the the circuit. However, sometimes I think to myself, isn't \$X_L=\omega L\$ then why can't I say \$X_L=\omega_0L\$ in the considered case?

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    \$\begingroup\$ Does a resistor have resistance, even when there's no voltage or current source connected to it? \$\endgroup\$
    – The Photon
    Commented Mar 31 at 23:57
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    \$\begingroup\$ That is like saying if your car runs out of gas (the energy source) then the car disappears. :) \$\endgroup\$
    – RussellH
    Commented Apr 1 at 0:26

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The question you're asking is basically the same as "if a tree falls in the forest and nobody is around to hear it, does it make a sound?".

Reactance is a property of an inductor or capacitor. It's not dependent on the presence of any AC sources--the presence of AC (with or without a defined source) just determines what frequencies are relevant.

A 1 μH inductor still has 6.28 Ω of reactance at 1 MHz, even if there's no 1 MHz signals in the system.

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The mechanical equivalent is an undamped spring and mass. Its resonant frequency is still defined by mass and the spring constant and, they have equivalent reactances just like any AC circuit. Their mechanical reactances do not depend on any external force just as electrical reactance does not depend on the externally applied voltage.

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While resistance is the opposition to the flow of current the reactance is the opposition to the change in current. So where ever there is a change in current in inductor or capacitor there will be reactance. Sometimes reactance is needed in calculation and sometimes it's not needed.

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