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A cylindrical conductor of length $l$ and uniform area of cross-section $A$ has resistance $R$ . Another conductor of length $2 l$ and resistance $R$ of the same metal has an area of cross-section

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\frac{A}{2}

\frac{3 A}{2}

2 A

3 A

answer is C.

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Detailed Solution

A cylindrical conductor of length

l

and uniform area of cross-section

A

has resistance

R

. Another conductor of length

2 l

and resistance

R

of the same metal has an area of cross-section

2 A

.
Given data in the problem,
Length of conductor,

L = 2 L

We know that,

R = ρ (\frac{L}{A})

Resistance of conductor of length

l

and uniform area of cross-section

A

R_{1} = ρ_{1} (\frac{L_{1}}{A_{1}})

\Rightarrow R = ρ_{1} (\frac{L}{A})

Resistance of conductor of length

2 l

R_{2} = ρ_{2} (\frac{L_{2}}{A_{2}})

\Rightarrow R = ρ_{2} (\frac{2 L}{A_{2}})

As resistance remains same, Equating above equations we get,

R_{1} = R_{2} = R

\Rightarrow ρ_{1} (\frac{L}{A}) = ρ_{2} (\frac{2 L}{A_{2}})

Density remains same in both cases as material doesn’t change.

\Rightarrow ρ (\frac{L}{A}) = ρ (\frac{2 L}{A_{2}})

\Rightarrow A_{2} = 2 A

So, the cross section of the metal is

2 A

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