Which bulb lights first? 9

[lyledunn]

I do a little lecturing on a temporary basis in a local college. Some time ago,one young, eager lad was keen to know the answer to this question: A bulb is placed at the remote end of a circuit of 10m length. There is a switch to operate the bulb. Now a similar circuit is 10miles in length, if both switches are operated at the same time, would there be any difference in the time it takes current to flow through the element, regardless of light output.
After some deliberation and chin rubbing, I offered my opinion. This seemed to asuage the lads thirst for a while. However, on throwing the question up in conversation during tea break in the staff room, I was amazed to see significant differences of opinion amongst the other lecturing staff!
Would you care to offer your opinion?



Regards,

Lyledunn

 

[rbulsara]

Electricity travels at the speed of light!

So now you can calculate the time difference! (if any).

(this of course ignores the voltage drop!).

 

[gordonl]

My first thought would be what goes in comes out, although the electrons move at a finite speed, I would think they would all start moving at once. But a pulse takes time to travel down a transmission line, so the leading edge must take time to travel as well.

 

[SidiropoulosM]

Since the switches are placed at the bulb end, both bulbs will light at the same time. Voltage is present at the bulb end of the wire even with the switches off.

 

[buzzp]

It is not clear where the switches are located. I assume both switches are located near the source of power with 10m length of wire to one bulb and ten miles to the other bulb. I think both would come on at the same time. The electrons and holes all start moving in the wire at the same time so I think they come on at the same time since the broken wire (switch) is the same length from one terminal to the outgoing terminal on the switch. Geez, I hope I get this right

 

[BJC]

I don't know wire sizes and current but the light at the end of ten miles may not see enough voltage to even glow.
Did you ever give them this problem?

Ole takes his light bulbs from Minnesota back to Norway where the voltage is 220 volts. He doesn't want to waste them so he wires up a couple of sockets in series and screws in a 60 and a 100 watt 110 volt bulbs and plugs them into the 220 volt outlet. How many watts does the circuit draw?

or

There is a metallic conduit going underneath a wide river with 7 wires (same
color and size) through it. Your job is to identify the wires and lable #'s
1-7 at each end. You are supplied with a boat w/ motor, wirenuts, locknuts,
continuity tester, wire tags, tape. You may use any basic electrical tools
you think necessary.
Here's the catch... You are only allowed to go across the river once and
then back. How would you do it?

 

[DanDel]

BJC:
1. 150W

2. Mark one wire #1, ground it. Mark another #2, leave it open. Splice and isolate two more, and then splice and isolate the last three.
Go to the other side, mark the grounded wire #1, mark the two wires that test continuous #3 & #4(it doesn't matter which), mark the three wires that test continuous #5, #6 & #7(again, it doesn't matter which). Mark the wire which tests open #2. Connect the wires you marked #3 and #5 to ground. Connect wire #6 to wire #2.
Go back to the other side. Open the splice with the two wires, the grounded one is #3, the other is #4. Open the splice with the three wires, the grounded one is #5, the one continuous to #2 is #6, and the last one is #7.

 

[Laplacian]

Electricity does not travel at the speed of light. People can run faster than single electrons flow through copper.

Both bulbs would energize at the same time if the circuit was ideal, no inductance or capacitance. The electrons are already in the conductors so they start moving instantaneously.

Imagine a water hose with perfectly rigid walls and an infinite source available. One hose is 10m long, the other 10 miles. If the hoses are initially full of water (electrons), the moment you open the valve water runs out of both the short and long hose ends simultaneously.

 

[jwerthman]

Very good DanDel. You get a star for that!

 

[DanDel]

Thanks, jwerthman!

 

[BJC]

DanDel
Try the light bulbs again.

 

[jghrist]

Laplacian,

Imagine your full water hose doesn't have a constant pressure at the valve (like dc voltage), but has a vibrating membrane (like ac voltage). Now when the membrane starts to vibrate, will the pressure changes occur instantly at the other end of the hose? No, what you are doing is transmitting sound and it will travel at the speed of sound in water.

Similarly, the ac electrical current will not start to flow instantaneously at the end of the 10 mile wire. "The velocity of propogation of an electromagnetic disturbance in air is the same as that of light, namely 2.998x10[sup]10[/sup]. The only difference for transmission lines is that the conductor provides a guide. In terms of the constants of the line, this velocity is equal to 1/sqrt(C·L)."[sup]1[/sup] For most cables, this is about 1000 ft/µs.

1. Westinghouse T&D Book.

 

[GordS]

All circuits have capacitance to ground (imagine an infinite number of capacitors from the wire to ground). As you apply voltage to one end of the circuit, the first thing that is seen by the voltage is a capacitor that is uncharged. It therefore acts as a short for all of the electrons until it gets charged. Then the next capacitor to ground needs to get charged. The result is that wavefroms take a finite time to travel through conductors. The speed is related to the distributed inductance and capacitance of the circuit. This will be the approximately the speed of light for overhead wires and less for insulated cables ( in the range of 50% that of overhead lines - check the IEEE Red Book section on surge voltages) So the two lamps will not light at the same time.

 

[illiterate]

An interesting link for electrical misconceptions is

http://www.eskimo.com/~billb/miscon/elect.html

 

[peebee]

Yup, I agree, the signal will travel at roughly the speed of light, or some percentage of it as described above. This is essentially a transmission line, and there will be a small but finite delay in the light lighting.

Laplacian's analogy of the water hose is a good one. But he's simplified both the water hose and the electrons just a bit too far. The water will not exit instantaneously. The analogy needs to be taken further:

When the valve is opened, the first water molecule will squeeze into the next one, and that second one will bounce off it and squeeze into the third, and so on. This will proceed as a wave down the hose. The speed of the wave will be equal to, or a percentage of, the speed of sound in water.

Now we got us a tight analogy.

 

[alehman]

If I remember my electromagnetics,

V(% speed of light) = 1 / sqrt(k)
k = relative permitivity of insulation = 1.0 for air

Also, Eistein's Theory of Special Relativity states that no signal or other conveyence of information can travel in excesss of the speed of light in a vacuum.

 

[jbartos]

Suggestion: Some relationships are posted without dimensions, e.g.
2.998x10E10 is in centimeter/second
2.998x10E8 is in meter/second
2.998x10E5 is in kilometer/second

 

[electricpete]

alehman - I think both the permitivity and the permissivity are needed.

The original question is an interesting one. I have to scratch my head a little to try to figure out how to combine the wave and circuit elements of the problem.

Perhaps another refinement in considering the whole question: doesn't the very long wire have a large inductance which will slow the rate of increase of current?

Lyle - I seem to remember you from a long time ago at alt.engineering.electrical. Are you from down under?

 

[jbartos]

Suggestion: Visit

http://www.radioelectronicschool.com/downloads/howfast.pdf

for electricity flow and the speed of electricity flow under different angles/theories

 

[busbar]

Crudely, at 1ns/foot, then ~30ns difference.