The full, detailed explanation to that question is quite long, but let's try a quick answer.
If we apply D.C. to a capacitor, there will be a brief pulse of current as the capacitor charges, then the current will taper off until it reaches zero when the capacitor is fully charged. The time taken to charge will depend upon the actual value of capacitance and the overall resistance of the circuit (including the source).
We define the time constant as the time it takes for the voltage on the capacitor to reach 63.2% of its final value, and it can be calculated as:
t = R * C
where R is the resistance in ohms and C is the capacitance in farads. For most practical purposes, we can consider the capacitor to be fully charged after a period of 5t.
Applying D.C. to an inductor gives us a somewhat different result. The inductor tries to oppose changes of current, so the current starts low and we see it increase gradually. Again, we define the time constant as the period it takes for the current to reach 63.2% of its final value:
t = L / R
where L is the inductance in henrys.
After approx. 5t seconds the current will have reached its final, maximum value, which will be determined by the overall resistance of the circuit (including the inherent resistance of the coil).
Applying A.C. results in a rather different result, since the A.C. waveform is continually varying.
For an inductor, we can determine the reactance ("A.C. resistance" if you will) of the coil from the formula:
X = 2 * pi * f * L
where f is the frequency. That means that for any given coil, as you increase the frequency the reactance will increase and thus the current will decrease.
For a capacitor, the relationship is the inverse:
X = 1 / (2 * pi * f * C)
So for a capacitor, an increase in frequency results in a decrease in reactance, with a corresponding increase in current.
When we put capacitance and inductance together in a parallel combination, it follows that the voltage across each component at any given moment must be the same.
However, that charging action means that in a purely capacitive circuit the current leads the voltage waveform by 90 degrees. Similarly, the current in a pure inductance lags 90 degrees behind the voltage. That means that for a parallel LC circuit, the current in the L section is 180 deg. out of phase with that in the C section.
The currents oppose each other, and therefore the overall reactance of the circuit is the difference between that of the coil and that of the capacitor.
Because inductive reactance increases with frequency while capacitive reactance decreases, there will be some specific frequency at which XL and XC are equal. This is the resonant frequency of the LC combination, and at this frequency the currents in L and C are exactly equal. because they are 180 out of phase though, they completely cancel out as far as the external circuit is concerned.
Thus at the resonant frequency, the parallel LC circuit appears as an infinitely high impedance and no current will flow. (In a theoretically perfect circuit that is -- In practice, of course, we can never quite achieve that.)
The resonant frequency can be calculated from:
f = 1 / ( 2 * pi * SQRT(L * C) )
Now, altering the value of the parallel resistance will have no effect on the actual resonant frequency of the circuit, but it will change the overall characteristic, since of course there will always be a parallel path for the current around the tuned circuit.
The lower the value of the parallel resistance, the less sharply defined will be the dip in current at the resonant frequency. A parallel resistance is often used across an LC combination in this way in radio circuits to deliberately broaden the frequency response.
[This message has been edited by pauluk (edited 09-16-2006).]
