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Which bulb lights first? 9

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lyledunn

Electrical
Dec 20, 2001
122
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
 
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The inductance of the wire will certainly limit the rate of rise of the current. I guess we need to go back to the original question and clarify what is being asked.

//would there be any difference in the time it takes current to flow through the element, regardless of light output.//

It seems like we are only concerned with when the initial voltage wavefront arrives at the lamp.

electripete - I'm not sure about permissivity (permeabiltiy?). Can you elaborate?
 
Certainly my remembering old physics classes, electrical current in a conductor is essentially an electromagnetic wave. And every material has a refractive index e.g. speed of light lower than c which is defined in a vacume. So who knows the "speed of light in a conductor?" (need to specify materials and impurities, probably crystal structure also I suspect?). Looks like gords may have it otherwise. [pipe]
 
I have seen a lot of statements about the speed of an electric signal in a cable here. The cable is a transmisson line and the speed is usually between 60 and 70 percent of the speed of light. The fact is being used in TDR for locating faults in cables (do a google on "cable radar") and my experience is that using 2/3 of vacuum c gives very accurate results. The nice thing about this is that a TDR measures the time to target and the time back to the instrument so the simple formula to calculate distance to fault is 100 metres/microsecond.
 
I did some more research on this and basically stand by my orignal post. Electripete has a good point, permissivity (permeability) should be included for a general formula. Most transmission lines have non-magentic medium, so permeability can be safely ignored for these cases.

From J.D. Kraus, "Electromagnetics",
Velocity of propagation in any transmission line is a function of the permeability and permittivity of the surrounding medium. The following can be derived directly from Maxwell's equations:

v[sup]2[/sup] = 1/ue
where v = velocity, u=permeabiltiy, e=permittivity
or
v = 1/sqrt(ue)
and
vr (the velocity relative to light) = 1/c*sqrt(ue)
where c = velocity of light in a vacuum

In the case of a non-magnetic medium (e.g. air), u app.=u0 and the above reduces to

vr = 1/sqrt(k)
where k = e/e0, the relative permittivity of the medium

For air, e app.=e0, so vr app.= 1, the speed of light

With polystyrene dielectric (e.g. coaxial cable), k = 2.7 and
vr = 1/sqrt(2.7) = 0.61

jbartos and busbar are correct assuming the transimission line is in air. skogsgurra's 60 to 70% is correct of typical solid dielectrics.
 
BJC,
Your light bulbs - I reckon 0 watts.
Maybe 150 watts instantaneously, until the 60 watt lamp
pops!! I don't really want to calculate how long that will take after the switch is thrown !!

KVKEV
 
KVKEV
Go to the head of the class. There are sure to be arguement about voltage tollarance etc. But the question is academic. It's just a quiz or homework problem to teach students to follow through and look at all the details of a problem.
 
It would be hard to calculate that momentary power for BJC's bulbs because the resistance goes up as the voltage (filament temperature) increases.
 
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