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A tightly coiled spring having 75 coils, each 3.50 cm in diameter, is made of insulated metal wire 3.25 mm in diameter. An ohm meter connected across its opposite ends reads 1.74 Ω. What is the resistivity of the metal?


A tightly coiled spring having 75 coils, each 3.50 cm in diameter, is made of insulated metal wire 3.25 mm in diameter. An ohm meter connected across its opposite ends reads 1.74 Ω. What is the resistivity of the metal?
Solution:
Given,
number of turns, n = 75
diamter of spring, d1 = 3.50 cm
radius of spring, r1 = 1.75 × 102 cm
diameter of metal wire, d2 = 3.25 mm
radius of metal wire, r2 = 1.625 × 103 m
resistance of metal wire, R = 1.74 Ω
resistivity of metal wire, ρ = ?
Let, l be the length of metal wire.
Now,
length of metal wire=length of spring coil=n×2πr1=75×2π×1.75×102l=8.25m Again,
R=ρlAρ=RAl=1.74×πr228.25=1.74×π×(1.625×103)28.25ρ=1.75×106Ωm Hence, the resistivity of the metal wire is 1.74×106 Ωm.
Detailed explanation of this numerical problem can be found in the video below. ( Skip to 11:08 ).

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