[Physltest] [Phys-L] Re: ISOLATION TRANSFORMER

[John Denker <jsd@AV8N.COM>]

David Abineri wrote:
> Why is there no current when shorted? Is there not still a
> voltage being induced in the secondary?

Sure there are voltages.  But voltages don't tell the whole
story, and are not by themselves sufficient for figuring
out the whole story. You need to figure out what the currents
will be, and for that you need to know the impedances as well
as the voltages.

To say the same thing another way, you need to think about
load lines and Thévenin equivalents.  You can't talk about
"the" voltage without qualification, because the open-circuit
voltage is not the same as the voltage under load.

At this point the canonical advice is to draw the circuit
diagram ... but that's easier said than done, because the
relevant _ideal_ circuit diagram has infinite impedances
in critical places, and infinity is hard to think about.
So what you really want is the non-ideal circuit diagram,
and that's not easy, because most people don't have the
training and/or experience to know what are the relevant
non-idealities.

So I'll give you a non-ideal circuit diagram that is
sufficient to explain the main ideas:

.            white                          red
.      -----------------$    $---------------------   o
.                       $    $       |              --|--G
.                       $    $      === c2           / \
.                       $-||-$       |
.                       $ c1 $       G
.                       $    $
        -----------------$    $---------------------
.        |   black                   |       blue
.        |                          === c3
.        |                           |
.        G                           G

The black and white wires are the ordinary electrical
service.  The black wire is tied to ground (G) at the
place where the service enters the building.

Ideally, the capacitors (c1 c2 c3) would have zero
capacitance i.e. infinite impedance, and would be
neglected.  These are not intentional or desirable
elements of the circuit, but rather they are forced
on you by the real-world physics.

1) If we assume c2 and c3 are negligible compared to c1,
the open-circuit voltage on the red wire will be roughly
115Vac relative to ground.

Now suppose our hapless victim, whose right hand is
already grounded, reaches up and touches the red wire.
He becomes part of a complete circuit.  This circuit
has a series impedance of omega c1 (plus some small
impedance of the victim himself), so the current in this
circuit is at most (omega c1 * 115V).  Assuming c1 is
rather small, this is a rather small current, not enough
to cause harm ... probably not even enough to be noticed.

The victim makes a voltage divider with c1.  The voltage
Vr under open-circuit conditions was 115Vac, but when
loaded by the victim it gets divided down to some tiny
value.

2)  If we assume c2 and c3 are comparable to each other
and c1 is negligible in comparison, then under open-circuit
conditions the red wire will sit at Vr ~ 58Vac relative to
ground.

Again suppose our hapless victim, whose right hand is
already grounded, reaches up and touches the red wire.
He becomes part of a complete circuit.  We anticipate
there will be another voltage divider, which means there
will be very little voltage across c2, hence c2 will
make a negligible contribution to the current.  So we
focus on c3.  The current will be (omega c3 115V).  If
c3 is small enough, the victim will not be harmed.

Note that the voltage-divider that reduces the voltage
across c2 increases the voltage across c3.

The remaining cases are left as exercises for the
reader:

3) As in case (1), assume c2 and c3 are negligible
compared to c1.  Find the open-circuit voltage on
the _blue_ wire this time.  Then find the short-circuit
current if the victim touches the blue wire while
touching ground with the other hand.

4) As in case (2), assume c2 and c3 are comparable and
c1 is negligible in comparison.  Find the open-circuit
voltage on the blue wire, and the short-circuit current
if the victim touches the blue wire while touching ground
with the other hand.

5) Find the relevant open-circuit voltage and estimate the
short-circuit current if the victim touches the red wire
with one hand while touching the blue wire with the other
hand.

======================================

The high-level lesson here is that when analyzing circuit
safety or circuit noise and interference, the first step
is to draw the circuit diagram including the non-ideal
elements of the circuit.  That's the hard part.  It requires
some nontrivial expertise, because there are in principle
an infinite number of possible nonidealities, and you have
to figure out which ones are relevant.  This is where physics
training comes in handy:  you get to estimate the value of
odd-shaped _physical_ capacitors and inductors, which is
very different from determining the value of a manufactured
component.  The next step is easy: once you've got the diagram,
you can analyze it just like any other circuit diagram.

To say the same thing another way, real circuits have
nonidealities that violate the spirit of Kirchhoff's
laws.  You can, however, in many cases bring things back
to some semblance of Kirchhoff form by adding to the
circuit diagram an assortment of "parasitic" elements
such as c1, c2, and c3 in my diagram above.
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