Voltage Drop Question

[Nick]

The resistance of the cable is 0.054 ohms, the bulb dissipates 55W @ 12.6V so it draws 4.37A and the cable drops 235mV, i.e. only about 2% of the total - within the limits of experimental error, this effect can probably be ignored.

14.4V is 14% higher than 12.6V. The graph you used shows that 15% over-voltage from nominal results in a current increase of about 10% (for heaters in a vacuum - remember this is not perfect as heaters tend to glow RED not white hot), i.e. the voltage drop will now be about 260mV, i.e. now only about 1.8% of total and again, can be ignored.

I wrote a calculator some years back to compute the necessary PCB track sizes to carry various currents within the constraints of set temperature rises and the various ANSI standards... Its not geared particularly to cable and doesn't compute skin effect impact, but its pretty accurate for low frequencies (e.g. DC ! ) (*)

ANSI IPC-2221A PCB Trace Width Calculator

The calculator agrees with your cable resistance of 0R054 (3m * 1mm^2 Cu) and shows that the cable will increase in temperature by about 0.2C above ambient and dissipate about 1.3W

(*) It's become a popular page in the last 10 years or so - It gets 10,000 hits a month

[Mark Hennessy]

All very interesting, the question came about when I was asked to explain how to work out what cross sectional area conductor would be needed when adding auxiliary stuff to a vehicle, nothing specific was specified but I used a 100 watt load as an example for a nominal 12 v system, that would be a current draw of 8.3 amps, a 1 mm cross sectional area conductor (standard PVC auto cable) would just about cope with that but the voltage drop over say 3 metres or so would be around 0.45 volts, the general consensus for voltage drop in vehicles for auxiliary stuff seems to be a maximum drop of 3% of the supply voltage if possible so although a 1 mm cross sectional area conductor would probably just about pass from a safety aspect it wouldn't pass from a voltage drop aspect so I mentioned a general rule of thumb that I have used in the past, choose a conductor that has a cross sectional area that's double that of a conductor that has a current rating the same as the load current or near to it as possible.

The question then came up about working out the voltage drop more precisely for a couple of different supply voltages and could it be done without a test meter, nothing load specific apart from the fact it would be a filament bulb, the parameters used in my earlier posts were chosen at will to illustrate the problem.

Lawrence.

Ah, OK.

So, for ways to be very precise about it, assuming you are allowed to characterise the light bulb first, my opening paragraph suggests how to go about it.

In practice, companies will either follow established "rules of thumb", or will do a bit of R&D and derive their guidelines for generations of subsequent engineers to follow. Experience will reinforce or modify these rules of thumb. I suppose that in some cost-sensitive industries - like mass-market car production - there will be pressures to save every fraction of a penny, and the temptation to go to a thinner cable might need some justification?

In engineering, it is possible to calculate almost anything with the right input data. But generally, it's much easier to use more "approximate" methods, like Nick and I both did.

Academics might want answers with 3 digits of precision, determined via complex maths, but generally this is about making the poor student suffer the maths (which may or may not have any long-term value!).

Conversely, real-world engineers with a developed "sense" of engineering will understand that there is no point aiming for such precision in many circumstances. A classic example is a transistor circuit, where a student might calculate that you need a 3.782 MOhm bias resistor because of the given value of Hfe - that student doesn't yet realise just how shockingly variable Hfe actually is. Let alone the tolerances of the resistors and power supply and transistor Vbe.

I do have a 6.5 digit bench multimeter at home, but it only gets used for very specialist jobs - most of the time, 3 digits is plenty. When you have uV resolution, interpreting the readings takes some skill - forget about the notion of a stable reading like you get with the 6,000 count Flukes et al! Noise, thermal potentials, thermal drift - it's all there in the reading, and really messes with your mind!

3.14 is accurate, but not precise.

3.15018912432 is precise, but not accurate.

I'd suggest that measuring a car headlamp bulb in order to produce a curve like you posted earlier would be pretty tricky in itself. What sort of accuracy would it yield, even with the best test gear? How many samples would you need to measure to determine the tolerances of the filaments? From how many manufacturers?

Still, an interesting thought experiment...

Enough of my ramblings - all the best

Mark

[pwdrive]

Thanks for the replies everyone, I used 3 decimal places because I guessed millivolts would crop up somewhere, I've noticed that 1mm CSA thin wall vehicle cable is rated twice that of standard PVC vehicle cable in current terms so that must be down to the insulation, I think the breakdown voltage is lower though, 50 to 60 volts seems to be the consensus on the web.

Lawrence.

[Nick]

Its more likely to be to do with its ability to dissipate heat due to the thinner insulation. Bundles of wire can easily melt with surprisingly small currents - the cables in the middle of the bunch can't lose heat, so melt.

Ideally, you want tough, thin, insulation that is rated a few times higher then you will experience - in this case there is no point having 1000V cable when you are unlikely to see anything over 20V. Thin PTFE cable is good as it is extremely tough, dissipates heat easily (thin walls), is unaffected by high temperatures (good to 250C plus), resistant to chemicals found in cars (salt, hydrocarbons etc.) and easy to "pull" through gaps..

[pwdrive]

Somethings dissipated some heat here, not long had a humdinger of a lightning strike close to us.

Lawrence.

[Skywave]

Just a follow-on from Mark's post #12.

In the 'The Radio Laboratory Handbook', by M.G. Scroggie, B.Sc., M.I.E.E., (6th. ed, 1954), M.G.S. has a chapter devoted to 'The Fundamental Principles of Measurement'. It is a thought-provoking chapter, and in my opinion, this chapter should be read by anyone who is involved in any aspect of Engineering, not just electronics. The sub-sections of this chapter include the following:

Measurement versus Guesswork,
False Assumptions,
Direct Observation or Instrument Readings ?,
Disentangling the Conclusions,
Personal Errors,
Reproducing Working Conditions,
and
Accuracy and Precision.

In that last-named sub-section, M.G.S. provides an interesting comparison of, and the difference between, accuracy and precision.

Apart from all that, this book, although now quite dated with obsolete circuits & specific measurement techniques, does illustrate the attitude and mind-set of a capable and trained engineer. Its title is a bit misleading, since throughout the whole of the text, the Philosophy of Engineering is subtly entrenched. It's not just about 'The Laboratory': it's also about who does what, why and how in that laboratory. It's a very good read by any set of standards and, in my opinion, should be in every electronics engineer's book-case.

Al.