Question

What is the relation between diameter of wire and resistance?

Answer 1

Answer:

inversely proportional to the square of diameter

Explanation:

The electric resistance of a metal wire is given by this correlation :

R = ρ x ℓ / A

Where, R is the resistance of the wire (Ω), ρ is called the specific resistance (Ω・m), ℓ is the length of wire, and A is the total cross-sectional of the wires (m²). Since the cross-sectional area of wire usually takes the shape of a long tube, its cross-sectional takes the place of a circle. Hence, the area of a circle, A = π r² =  ¼  π d².

Substituting this correlation into the first correlation, we will get

R = ρ x ℓ / (¼  π d²) = 4 ρ ℓ / (π d²).

So, it is now safe to say that the resistance of wire is inversely proportional to the square of the diameter. Hope this helps.

Regards,

Guru of Shinjuku Learning Support

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