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?
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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