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What will be the resistance of wire having diameter $2 D$ and length $4 L$ if the resistance of a old wire of the same material having diameter $D$ and length $L$ is $R$ .

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2 R

R

\frac{R}{2}

\frac{R}{4}

answer is B.

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Detailed Solution

R be the resistance of wire having diameter

2 D

and length

4 L

if the resistance of a old wire of the same material having diameter

D

and length

L

R

.
Given,
From the formula of resistance,

R = ρ \frac{L}{A}

[Where

ρ = resistivity; l = length of conductor; R = resistance]

A = area of cross section

We know that

A = π r^{2}

and

r = \frac{d}{2}

R = ρ \frac{L}{π {(\frac{D}{2})}^{2}}

------------ (1)
Now Resistance of second wire (R’)when

D = 2 D and L = 4 L

R' = ρ \frac{4 L}{π {(\frac{2 D}{2})}^{2}}

R' = ρ \frac{4 L}{π {(\frac{4 D}{4})}^{}}

R' = ρ \frac{4 L}{π {(\frac{D}{2})}^{2}}

ρL \frac{1}{π} {(\frac{D}{2})}^{2}

-------------------- (2)
Comparing (1) and (2)

R_{1} = R

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