A 1 kg piece of copper is drawn into a wire 1 mm² thick, and another 1 kg copper piece into a wire, 2 mm² thick. Compare the resistance of these wires.

2:1

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4:1

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8:1

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16:1

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Solution

The correct option is B
4:1

The volume of wire = length x cross-sectional Area. As the mass and density is the same, the volume is constant.

Since volume is same in both the cases, $l_{1} A_{1} = l_{2} A_{2}$

$A_{1} = 1 m m^{2}$ and $A_{2} = 2 m m^{2}$ we get $l_{1} = 2 l_{2}$

The length of the second wire will be half the length of the 1st wire.

Using R = ρ $\frac{L}{A}$ ,

$R_{1}$ = ρ $\frac{l_{1}}{A_{1}}$ , $R_{2}$ = ρ $\frac{l_{2}}{A_{2}}$

$\frac{R_{1}}{R_{2}}$ = $\frac{l_{1} A_{2}}{l_{2} A_{1}}$

Substituting $l_{1} = 2 l_{2}$ ,

$\frac{R_{1}}{R_{2}}$ = $4 : 1$ ,

We get the resistance of the 1st wire is 4 times the resistance of the 2nd wire.

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