Re: [Phys-l] home wiring catastrophe

[John Denker <jsd@av8n.com>]

On 05/17/2007 06:35 PM, Carl Mungan wrote:

> While working on one of those cubical boxes that distribute power into local houses (for
> underground wiring, as we have in our subdivision), the power company accidentally severed the
> neutral line. This fried the circuit panels (and possibly the entire 120-V wiring system) in 5
> houses, actually lighting one of them on fire. Sadly, these 5 houses have been declared unsafe
> and the residents have been living since then in hotels.

...

> I'm of
> course unhappy with the idea of voltage being carried and prefer to think about currents.

1) To specify the circuit condition, you need to know two
things:
 -- voltage and current
 -- voltage and resistance
 -- current and resistance
 -- whatever

Knowing only one thing doesn't get the job done.  See below.

2) Some good advice: draw the circuit diagram.

I always tell my students:  Experts draw the circuit diagram.
Why is it that students think they can get by without drawing
the circuit diagram?

In my diagram,
  http://www.av8n.com/physics/img48/house-circuit.png
Z0 through Z4 represent the parasitic series resistances of the
wires in the walls of the house.

The rest should be pretty self-explanatory.

3) It also pays to draw the "load diagram" such as
  http://www.av8n.com/physics/img48/load-line.png

The green box represents the normal operating envelope:  no
element sees a voltage drop greater than 120 V, and no element
carries a current greater than 15 A.

The black dashed hyperbolas are contours of constant power
dissipation.

You can see that for low-impedance series-connected elements
such as Z1, the circuit breaker is all that is required to
protect that element.  The CB trips at 15 A, preventing the
Z1 load-line from leaving the envelope.  Line voltage doesn't
enter into this calculation;  the voltage drop across the Z1
element is limited by the CB current times the internal impedance
of the element.

In contrast, for a high-impedance element such as R3, all bets
are off when there is a fault in the neutral wire (Z0).

Note that there can be an imbalance, such that R1 and R2 (and
all other loads on the "A" side if the circuit) can gang up on
R3 such that the supposedly-neutral side of R3 is effectively
dead-shorted to the "A"-side hot wire, with negligibly small
resistance and negligibly small chance that any "A"-side CB
will trip.

Meanwhile, the "B" side of R3 is still connected to the "B"-side
hot wire, so element R3 sees 240Vac across its terminals.  If
we (temporarily) assume it is Ohmic, it will dissipate four time
as much power as it was designed for.  At this point there is no
reason to expect CB3 to trip.  If you are lucky, there will be
some sort of fuse in series with R3, and the fuse will blow before
R3 sets your house on fire.

  As an aside, note that when R3 burns to ashes and/or the fuse
  blows, it removes R3 from the "B" side of the circuit, increasing
  the imbalance.  So it is quite possible to have a runaway condition,
  where the problem gets worse step by step.

Chunks of silicon are non-Ohmic;  their conductivity increases as
temperature increases.  Diode current is exponential in voltage ...
not to mention grossly nonlinear things like Zener breakdown and
other types of breakdown.  That means that if you put 2x the voltage
across a semiconductor device, you will might well draw /more/ than
2x the current, dissipating more than 4x the power, i.e. a situation
even worse than shown in my load diagram.



Now consider what happens if/when CB3 opens.  There will be a gap
between the contact points, and an arc across the gap.  The gap
and other details have been designed so that they suffice to
extinguish the arc when there is 120V driving the arc.  A higher
voltage arc will be harder to extinguish.  Again the situation
could be highly nonlinear;  indeed it could be a Micawber problem:
if the arc can just barely be cooled enough to go out, you're fine;
if the arc can just barely not be cooled enough, you've got a big,
big problem.


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

That isn't the whole story, but it should be enough to:
  a) put you on the right track if you want to do a fuller analysis, and
  b) convince you that a fault in the neutral wire is a bad, bad thing.