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A series-connected loading coil used in an antenna circuit with sufficiently high Q has a substantial voltage-multiplication effect at resonance. This high RF voltage causes a significant amount of current to flow through the antenna capacitance of the short antenna, and this capacitor current flows through the radiation resistance, which is in series with the antenna capacitance.

A loading coil connected in parallel with the antenna capacitance does not have a voltage-multiplication effect, and therefore the required high-voltage to get sufficient RF current through the antenna capacitance must come from the transmitter output. If the high-voltage RF source has a high impedance, a parallel loading coil is necessary to resonate with the antenna capacitance in order to provide a high-impedance load that does not significantly reduce the RF source voltage. The link in my post that Rich quotes goes to a part15.us Forum thread that (in part) describes my experiments with a vacuum-tube Part 15 AM transmitter that has a high impedance, high-voltage, source, with the loading coil and the antenna capacitance connected in parallel.

I have not attempted to make a high-voltage, low-impedance RF source, but if it were feasible to make such a source, driving the capacitance of a short antenna without a loading coil can be done. The phase difference between the voltage and current at the base of the antenna is near 90 degrees no matter whether a loading coil is used or not, because the antenna impedance is capacitive. A loading coil does not alter this phase relationship between voltage and current inside the antenna. To demonstrate this requires only ordinary circuit analysis. The following elementary example illustrates my point:

Just consider an ideal inductor in resonance with an ideal capacitor. In the inductor, the voltage leads the current by 90 degrees; and in the capacitor, the voltage lags the current by 90 degrees. In the series-resonant condition, the current through the inductor is in phase with the current through the capacitor, but the voltages across the inductor and capacitor cancel each other out. In the parallel-resonant condition, the voltage across the capacitor is in phase with the voltage across the inductor, but the currents in the inductor and capacitor cancel each other out. Drawing vector diagrams of what I described would enhance the understanding of what I am talking about.