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Q-32 Resistance of a copper wire of length 122.7m is 10 Ohms at 20 degree celsius. If the diameter of the wire is
0.5mm,what will be the resistivity of the wire at that temperature?
(3)
Answers
The resistivity of a copper wire with 122.7 m length, 0.5 mm diameter, offering 10 ohm resistance at 20°C is 0.15 × 10^-10 ohm m
• The formula for resistance is at a particular temperautre is :
R = p × (l / A)
Where R is the resistance offered by the wire at that temperautre,
p is the resistivity of the wire,
l is the length of the wire,
A is the area of cross section of the wire
• Given,
Resistance (R) of the copper wire = 10 ohm
Length of the wire (l) = 122.7 m
Diameter of the wire (D) = 0.5 mm
=> Radius of the wire (r) = D / 2 = 0.5 mm / 2
=> r = 0.25 mm
=> r = 0.25 × 10^-3 m
• Area of cross section of the wire = πr² = 3.14 × (0.25 × 10^-3 m)²
=> A = 0.19625 × 10^-9 m²
=> A = 1.962 × 10^-10 m²
• Now, substituting R, l, and A in equation (i), we get,
10 ohm = p × (122.7 m / 1.962 × 10^-10 m² )
=> (10 ohm × 1.962 × 10^-10 m² ) / 122.7 m = p
=> p = 0.15 × 10^-10 ohm m