I would be guessing. I understand a capacitor is two plates of semiconductor (i believe) each of which store oppositely charged ions. We use them for many things. The use that comes to mind is smoothing ac waveform when rectifying. Do I understand why the current leads voltage in a capacitor? No. You could’ve said voltage leads in a capacitor and I would say sounds good. The “why” has not clicked. i know just based off memorization that inductors have the opposite effect of capacitors in which lags which.
Allow me to try. Nothing as exotic as semiconductors. Physically, a capacitor is two sheets of aluminum foil separated by a sheet of waxed paper, rolled into a cylinder. Electrically, it behaves like a high-current rechargeable battery with a ridiculously short charge/discharge cycle.
Imagine a capacitor in series with a plain load, like a resistor, fed by an AC source. You can picture an AC sine wave, right? Okay, let's start the wave at 0v and begin ramping the voltage towards V+. Even though the voltage is still very low, the capacitor is charging at a high rate.
As the voltage wave settles at its peak, the capacitor is fully charged, so almost no current is passing through it, or the load. A the voltage starts to fall back towards 0v, the capacitor starts discharging, so its current rises, peaking as the voltage passes through 0v on its way toward V-.
As the negative peak is reached, the capacitor charges in the opposite direction until its current again drops to minimal. And again, as the voltage approaches 0v on its way towards +, the current approaches the peak, bringing us back to where we started.
Thus, the peak current through a capacitor occurs 90 degrees ahead of the peak voltage. With a purely-capacitive load, the entire current is fully 90 degrees leading. With a mixed load, the aggregate current is somewhere between 90 and 0 degrees leading.
Without going into detail about stored magnetism, etc., an inductor has the opposite effect, in that it resists change in the current, so it "charges and discharges," but the current tries to maintain despite the voltage dropping toward 0v, so the current peak follows.
The basic reason all this matters is, besides carrying the current that the load is converting into useful work, the conductors supplying the load also have to carry the wasteful charging and discharging current, so the entire electrical system must be sized to compensate.
Capacitance and inductance are collectively known as reactance, or reactive impedance. Impedance is made of resistance and reactance. The total power depends on the current through the total impedance, while the apparent power depends on the useful current.
The ratio of total power (expressed in volt/amps) to apparent power (expressed in watts) is known as the power factor, and is always 1.0 or lower. Capacitance and inductance can be used to counteract each other, which is called power-factor correction, or mitigation.
When power-factor correction is used, only the conductors (and equipment) between the load and the correction device need to be sized for the total power. This can save on installation and energy-bill costs, especially for industrial customers that pay more for poor power factors.
I hope that's enough to absorb for now. I have written a few other ditties, inducing one explaining how a neutral works.