A uniform wire is cut into 4 segments. Each segment is twice as long as the previous segment. If the shortest segment has a resistance of 4 ohms, find the resistance of the original wire.

The resistance of a piece of wire is directly proportional to its length, so we know that just like the length, the resistance of each segment is also twice the resistance of the previous ('earlier') segment.
So the resistances of the segments are:
4
8 16 32
and their total resistance before they were cut up was
(4 + 8 + 16 + 32) = 60 ohms

Answered by AL2006 | 2024-06-10

The original wire, cut into 4 segments with resistances of 4 ohms, 8 ohms, 16 ohms, and 32 ohms, has a total resistance of 60 ohms. Each segment's resistance doubles the previous segment’s due to their lengths. Thus, the overall resistance of the original wire is 60 ohms.
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Answered by AL2006 | 2024-12-26