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Physics Question on Capacitors and Capacitance

A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is stretched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

A

1:4

B

1:2

C

4:1

D

2:1

Answer

1:2

Explanation

Solution

A 1 m long wire is broken into two unequal parts X and Y

Rw = 2Ry
ρ2xA2=2ρ(1−x)Aρ\frac{2x}{\frac{A}{2}}=\frac{2ρ(1−x)}{A}
4x = 2(1 – x)

x1−x=12\frac{x}{1−x}=\frac{1}{2}
So, the correct option is (B): 1:2