The difference between impedance and resistance

Hi Bob,

In the case of a capacitor, the voltage between the two plates or conductors is proportional to the charge that has accumulated on them, the charges being equal but of opposite polarity on the two plates. Charge accumulates as a result of current flow between each plate and the circuit the capacitor is connected to. Therefore the charge and hence the voltage across the capacitor are proportional to the integral of current. Therefore (assuming an idealized capacitor model) an infinitely fast step increase in current will result in a gradual linear ramp-up of voltage.

In the case of an inductor, a change in current results in a change of magnetic flux, which results in a voltage being induced that opposes the change in current. See these writeups on Faraday's Law and Lenz's Law. Therefore, voltage is proportional to the rate of change (the derivative) of current; therefore current is proportional to the integral of voltage, and so a step increase in applied voltage will result in a gradual linear ramp-up of current.

Best regards,
-- Al

Bob: While reading the links keep in mind that the 'phase' difference is a way of describing the special case of the transfer function for a system when the input a sine wave and where the transients have died out (steady state).

Bob - the difference between the derivative in radians and degress is the scalar multiplier of k*pi. The key thing to note in my description is the word "directly". I found this description that should go into enough detail for you to understand what I was saying:

http://mathforum.org/library/drmath/view/54181.html

As for lead and lag, you can do a search for "ELI the ICE man" and the first few links that pop up offer good explanations.

Arthur

As to inductance the motion of a charge (which is current) causes a magnetic field.

Agreed. And the magnetic field can be shown to be a relativistic effect (Einstein - special relativity) of the pure electrical field. It all depends on your frame of reference.