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

Answers (1)

Let x be the length of shortest segment. 

Then lengths of four segments will be x,2x,4x,8x.

Here all the wires have same area of cross section and resistivities as they have been cut from the same, uniform wire, and are made of the same material respectively.

R of smallest wire with length x=

The resistance of a 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.

Their corresponding resistance will be 4 ohm,8 ohm,16 ohm,32 ohm

When these wires are rejoined to form the original wire, their equivalent resistance will be equal to the net resistance when four resistors of magnitude 4 ohm, 8 ohm, 16 ohm, 32 ohm are connected series. In series,

net R= R1 + R2 + R3 + R4= 4 + 8 + 16 + 32= 60 ohm.

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