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Resistance

Two wires of ...

Question

Two wires of the same material and same length have radii $r_{1}$ and $r_{2}$ respectively.The ratio their resistances and their resistivities will be

r_{2}^{2} : r_{1}^{2}

and 1 : 1

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r_{2} : r_{1}

and 1 : 1

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r_{2}^{2} : r_{1}^{2}

and 1 : 2

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r_{1}^{2} : r_{2}^{2}

and 1 : 1

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Solution

The correct option is A $r_{2}^{2} : r_{1}^{2}$ and 1 : 1
The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current whichflows through it. That is R=V/I.
The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area (that is square of the radius), and would be expected to depend upon the material out of which the wire is made.
The resistance of a wire can be expressed as $R = \frac{ρ L}{A}$ where,
rho is the resistivity of the wire,
L is the length of the wire,
A is the area of cross section of the wire, that is, square of the radius.
In this case, two wires of the same material and same length have radii r1 and r2 respectively are taken. So, the resistance will differ only in the square of the radius.
Hence, the ratio of the resistance would be ${r_{1}}^{2} : {r_{2}}^{2}$ and 1:1.

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