A nicotine wire has diameter 1.0 my and resistivity of 1.0 into raise to the power minus 4 ohm metre. Calculate the required length of this wire to make a resistance of 14 oh.
Answers
Given : A nichrome wire has a diameter of 1.0 mm and
resistivity of 1.0×10 ⁻⁴ ohm m .
To Find : The required length of this wire to make a resistance of 14 ohm
Solution:
R = ρ L/A
R = 14 ohm
ρ = resistivity = 1.0×10 ⁻⁴ ohm m
L = ?
A = area = πR²
R = radius = diameter/2 = 1.0 mm/2 = 0.5 mm
= 5 * 10⁻⁴ m ( 1 m = 1000 mm)
π = 3.14
A = 3.14 * (5 * 10⁻⁴)²
= 78.5 * 10⁻⁸ m²
=> 14 = 1.0×10 ⁻⁴ * L / 78.5 * 10⁻⁸
=> L = 14 * 78.5 * 10⁻⁴
=> L = 1099 * 10⁻⁴ m
=> L = 1099 * 10⁻² cm
=> L = 10.99 cm
=> L ≈ 11 cm
Hence required length of this wire to make a resistance of 14 ohm is 11 cm
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