J
[email protected]
- Jan 1, 1970
- 0
You won't be able to maintain a steady-state DC voltage drop
across a conductor with zero DC resistance, because that would
imply infinite current. However, the transient or AC-voltage
case the story is entirely different. Consider, for example,
my 10kV 300kHz ferrite-core transformer, which has 22 turns on
its secondary. The single-turn primary has 450 volts across
its ends. Since it's a thick band of 1"-wide copper, with for
all practical purposes, zero DC resistance, by your obviously-
incorrect understanding this is not possible. BTW, the current
in my transformer's single thick strip of copper is modest and
due almost entirely to activities outside the copper strip.
Let's assume the secondary is open-circuit so that it has no effect on
the the primary. When you apply 450V across the primary, that doesn't
mean the primary winding has a voltage of magnitude 450V through it
because total EMF = 450V - primary = rate of change of magnetic flux =
Lp*d(Ip)/dt. With static I, total EMF = 450 - primary = 0, and so
primary = 450V which, as you pointed out, would give an infinite
current for a 0R primary.
Where there is a changing magnetic field, the electric field isn't
conservative and so you can't assume that components in parallel will
have the same volage through them. Suppose you have a ring of 1R in a
uniform magnetic field normal to the plane of the ring. Suppose it
changes at a uniform rate so that it induces an electric field in the
ring with the total EMF around the the ring being 1V. The voltage
across a 0.1R segment = 0.1V is in parallel with the rest of the 0.9R
= 0.9V segment, yet the voltage drops are not the same. In a
conservative field where total EMF around ring = 0V, you can say
V_0.1R = V_0.9R.
Some people recommend this paper. If you want I'll email it to you.
R.H. Romer: "What do 'voltmeters' measure?
Faraday's law in a multiply connected region",
Am. J. Phys., 50, 12 (1982), pp. 1089-93