Take also, as a fact, the statement given above that the necessary E.M.F. at the actual terminals of the arc lamp may be accepted as a constant at 45 volts, and reverting to the equation given on page 40, C = E / R, and substituting these figures we get—
Current (10 ampères) = E (45 volts) / R (Resistance of Arc).
It is therefore obvious that under these exact conditions the resistance or back E.M.F. of the arc, as it is termed, must equal 4.5 ohms.
Now suppose the lamp left for a few seconds unattended, while the carbons are burning away and the arc is lengthening; in a very few moments the resistance will have increased, owing to the greater distance between the carbons, and we will suppose it to have become 5 ohms instead of 4.5.
The current passing will now be 45 / 5 = 9 ampères only.
In other words, a very slight lengthening of the arc has reduced the current, and therefore the light, by 10 per cent.
Not only so, but 45 volts being needed to maintain an arc of
normal length, it is insufficient to maintain a longer one, and in practice the effect of leaving an arc under these conditions to itself for even a few seconds is that it goes out, to the annoyance of the lecturer and the confusion of the operator.
It is just possible to work an arc lamp with a total E.M.F. of 45 volts by giving one's whole attention to it and never taking the hand off the feeding handle; but in practice no one with any experience would attempt it. The arc would almost certainly go out several times during the exhibition.
Now, take an example of a similar arc lamp consuming 10 ampères but worked from a supply of 200 volts.