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Question

A metal wire of length l and diameter d has a resistance R. What would be the resistance of another wire of the same metal and of the same length but having double the diameter?

This question was previously asked in
CDS I 2022 English Previous Year Paper (10-April-2022)
The correct answer is

R/4

The correct answer is R/4.

  Key Points

Electrical Resistance:

  • The electrical resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor.
  • The resistance of a wire is inversely proportional to the cross-sectional area of the wire.
  • That is, as the diameter of the wire increases, the resistance of the wire decreases, and as the diameter of the wire decreases, the resistance of the wire increases.
  • Area of the cross-section of the wire = \(πr^2 =~\frac{π}{4} \times d^2\)
    • Where d = diameter of the wire
  • The resistance of a conductor is given as  \(R = ρ\times\frac{l}{A} = ρl~\times\frac{4}{\pi d^2}\)
    • Where, ρ = resistivity (Ohm)
    • A = cross-sectional area of the wire
  • If we double the diameter, the resistance will decrease by 4 times. (Resistance is inversely proportional to the square of the diameter)
    • Since both wires are made of the same material, the resistivity will remain constant.
  • If the resistance of wire 1 having length l and diameter d is R, then the resistance of another wire 2 having length l and diameter 2d will be R/4.
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