Question

a piece of wire of resistance 4 ohm is bent through 180 degree at its midpoint and the two halves are twisted togther,then the resistance isquestion no 9

Answer 1

Follow the pic below
Answer is ¼ of the given resistance that is 1ohm

Answer 2

Answer:

Resistance of the bent wire is $4\Omega$

Explanation:

Given: Resistance of wire, $R=4\Omega$

General fomula of the resistance of a wire is given by,

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

where,

$\rho$ is the resistivity of the material of the wire,

$l$ is the length of the wire,

$A$ is the cross sectional area of the wire.

Now, when the wire is folded into a half, its new cross-sectional area becomes twice as big and its length becomes half as much as it was before. Resitivity remains same before and after bending of wire as it depends on the nature of the material of wire.

Let new, cross-sectional area is denoted by, $A' = 2A$

and new length be denoted by, $l'=2l$

New resistance of the wire = $R'=\rho\frac{l'}{A'}$

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

$\implies R'= \frac{1}{4} (\rho \frac{l}{A} )$

$\implies R'= \frac{R}{4}$

$\implies R'=\frac{4}{4} \Omega$

$\implies R'=1 \Omega$

Resistance of the bent wire is $4\Omega$

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