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Question

A 4 ohm resistance wire is stretched to double itself ,find the new resistance of the wire


Solution

Suppose the length of the wire and  its cross sectional area be L & A respectively. If it is stretched to double itself,then length will be 2L, the cross sectional area must halve to A/2.

Resistance R of a wire is linearly proportional to length, and inverse linear proportional to cross sectional area.
therefore, R = x * L/A
or 4 = x * L/A
or x = 4A/L

Now if lenght = 2L and cross sectional area = A/2
Then New Resistance R1 = x * 2L/(1/2A) = (4A/L) * 4L/A = 16 ohms
The new resistance will be quadruple
Ans.16 Ohms

 

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