Physical meaning behind an imaginary impedance

Impedance is the ratio of voltage to current. The imaginary value is caused by the phase of the current and voltage being different by 90 degrees.

To expand a little on Flatulent's reply -

Impedance is the sum of resistance, inductive reactance, and capacitive reactance.

Reactance is the property of an inductor or capacitor that opposes a change in current, or a change in voltage in the circuit. Note the word "change" - reactance only comes into play when the voltage and/or current is trying to change. We call changing current "alternating current" or "AC". So reactance is the AC "resistance" of an inductor or capacitor.

When you instantaneously change the voltage across an inductor, it takes a while for the current to change. The reason is the magnetic field that surrounds each turn of the inductor as the current begins to flow, and cuts through other turns of the inductor. That growing magnetic field cutting through the other turns creates an opposing current that slows the flow of the current trying to build because of the applied voltage. The opposition to current increase is the AC resistance mentioned above, and it happens such that the current is time delayed 90deg behind the applied voltage as measured by phase angle.

Likewise, an attempt to change the voltage across a capacitor is delayed by the current required to build an electrostatic charge separation on the capacitor plates. In this case the voltage is time delayed 90deg behind the current as measured by phase angle.

The delays mentioned above are caused by magnetic or electrostatic fields building. A resistor in the circuit has no delays between application of voltage and current flow, and would transform the applied energy into heat (Power = Voltage x current). In conceptual terms, the resistor is doing real work (getting hot), and the inductor or capacitor is doing imaginary work because they are just storing the energy supplied to the circuit as magnetic field or charge separation.

When we describe the total impedance as a mathematical equation, we use a vector equation because the current isn't in phase with the voltage in the various elements of the circuit and we need to describe that fact in the equation. Remember the discussion above - voltage and current are in phase in the resistance (that is current changes when voltage does), current is 90deg delayed in the inductor (delayed because of the opposing voltage generated due to increasing magnetic fields cutting through turns of the coil), and current is 90deg ahead of the voltage in the capacitor (because of the need to move electrostatic charge before there can be a voltage difference).

The 90deg phase angle in the impedance vector equation is represented by "j", which in vector equations is the square root of negative one (-1). So the total impedance is equal to the real part (resistance), plus a negative imaginary part for inductance (-jXl), and a positive imaginary part for capacitance (+jXc) > Z=R-jXl+jXc.

Please note that I have taken liberties above with the terms "work" and "energy" to get a concept across. The strict and proper defintions of those two terms as applied here would need more words to get across the same ideas.

this is really a very helpful post. Many thanks !

I agree. That explanation was epic.

I agree mostly except the last part starting from total impedance. There is no mentioning about how overall network is consist of. So, the total impedance is kind of misleading since "total" is undefined. I would suggest mentioning individual impedance of C and L. Also, Impedance of L is +jωL, and 1/jωC (= -j/ωC) for C. I believe the +-sign is wrong.

Yes I believe so.
But thanks both of you for the explanations.