Question

A wire of 1000ohm and length l is increased to twice it's original length calculate it's original resistance

Answer 1

Answer:

The original resistance of wire will be equal to 4000 ohm.

Explanation:

Suppose that the length and area of the wire is $l$ and A respectively.

$R = \rho\frac{l}{A}$

where, $\rho$ is the resistivity of the wire.

Given, the value of the resistance of the wire, R = 1000 ohm

If the length of the wire increased to twice then the area of wire will decrease to half.

Assume that l'  and A' are the new length and area of wire after stretching.

Therefore, l' = 2l and A' = A/2

Assume that R' is the new resistance of the wire:-

$R'= \rho\frac{l'}{A'}$

$R'=\rho\frac{2l}{A/2}$

$R'=4(\rho\frac{l}{A})$

$R' = 4R$

$R'=4\times 1000$

$R'= 4000$ Ω

Therefore, the original resistance of wire is equal to 4000 ohm.

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