Ken, the idea of the formula was to substantiate a reply to an objection regarding the choice of words of the OP.
I am no Richard Feynman, so I will not be able to be as clear as a professional teacher. Still, to make a long story short :
The concept of impedance is a generalization of the concept of resistance, i.e. the proportional relationship between current and tension. With a resistance, everything is simple : tension U is related to current I by the U=R.I relationship.
For a capacitor, U is related to the integral of the current over a period of time. But using mathematics in the complex world, integrating is "simply" dividing by j.w (assuming a sinusoidal current, and where j²=-1 and w or "omega" is the pulsation of the current). So one can write U=Z.I with Z=1/jCw.
Conversely, for a solenoid, U=Z.I with Z=jLw.
Therefore, in electronics, impedance is a generic term covering at once R,L and C. And asking for the impedance of a capacitor is another way of asking for its capacitance. Pretty much in the same way that asking someone for their address will give you the name of their hometown, and a bit more.
As for E=m.c², if I may, there might be a slight twist in your VHS or your recollection of it. To apply E=mc² to your baseball, you would have to thoroughly disintegrate said baseball, and the energy released (in the form of massless photons) would be m.c², m being the rest mass of said baseball. If you could accelerate the ball to lightspeed, its mass would change and things get pretty messy from here. But e=mc² is always true, even for a baseball at rest. And you cannot accelerate it to c², which is not a speed.
Hope this helps,
Nick.
I am no Richard Feynman, so I will not be able to be as clear as a professional teacher. Still, to make a long story short :
The concept of impedance is a generalization of the concept of resistance, i.e. the proportional relationship between current and tension. With a resistance, everything is simple : tension U is related to current I by the U=R.I relationship.
For a capacitor, U is related to the integral of the current over a period of time. But using mathematics in the complex world, integrating is "simply" dividing by j.w (assuming a sinusoidal current, and where j²=-1 and w or "omega" is the pulsation of the current). So one can write U=Z.I with Z=1/jCw.
Conversely, for a solenoid, U=Z.I with Z=jLw.
Therefore, in electronics, impedance is a generic term covering at once R,L and C. And asking for the impedance of a capacitor is another way of asking for its capacitance. Pretty much in the same way that asking someone for their address will give you the name of their hometown, and a bit more.
As for E=m.c², if I may, there might be a slight twist in your VHS or your recollection of it. To apply E=mc² to your baseball, you would have to thoroughly disintegrate said baseball, and the energy released (in the form of massless photons) would be m.c², m being the rest mass of said baseball. If you could accelerate the ball to lightspeed, its mass would change and things get pretty messy from here. But e=mc² is always true, even for a baseball at rest. And you cannot accelerate it to c², which is not a speed.
Hope this helps,
Nick.