On Nov 24, 10:14, Dave Woodman wrote:
> Let's try to keep this in accordance with real physical laws:- the
> current flowing in the wires will be inversely proportional to the
> resistance since the potential difference across them is the same.
So far, so good...
> The physical principle
> that causes the problem is that the power dissipated is proportional to
the *square* of the current. In case of any doubters -
>
>
> Ohms Law:
> I = V/R
>
> => V=IR
>
> Power dissipated:
> P = IV
>
> => P = I(IR)
>
> So, for example, if one cable/connector pair had twice the resistance of
> another, the second would dissipate four times as much power as the
> first.
Er, no. The current will NOT be the same in each case. If you're going to
use mathematical equations to argue, use the right ones :-)
Power dissipated (assuming steady-state DC):
P = IV
and I = V/R
=> P = V^2/R
So if one cable/connector pair has twice the resistance of the other, the
second will dissipate twice, not four times, the power (since V is the same
for both).
But even that analysis is over-simplified. The PSU provides a fixed
voltage (assuming it's running within expected limits). Part of that
voltage is dropped over the intended load, and part over the
cables/connectors. If the resistance of the cables or connectors goes up
(which is what happened) then the proportion dropped by the cable/connector
combination also rises (and the resistance also goes up slightly as the
temperature rises). This makes the situation slighly worse than my maths
above suggests, but not as bad as Dave suggested.
> If, as other posters have indicated, the bulk of the resistance is in
> the connector then the heating effect will be quite localised, and the
> home cooking lessons are on.
That's still true, of course, but the difference isn't as extreme as you
implied. In the cable looms that failed, it was the cables' insulation
that melted, but mostly near the connectors, and typically on all the 5V
cables, not just the longer ones. I remember some discussions in DECUSERVE
NOTES about it.
--
Pete Peter Turnbull
Network Manager
University of York
Received on Sun Nov 24 2002 - 07:25:00 GMT