Question

Resistance of a metal wire of lenghts 1 m is 26 ohm at 20 degree C. If the diameter of a wire 0.5 mm. what will be the resistivity of the metal at that temperature?​

Answer 1

Explanation:

r = radius, d = diameter, p = resistivity.

R = resistance , A = area, l = length

Here,

Area of wire = πr² = π(d/2)² = π(d²/4)

= d²π/4

we know,

=> R = p(l/A)

=> R(A/l) = p

=> R(A)(1/l) = p

=> 26(d²π/4)(1/1) = p

=> 26[0.5²mm² * 22/7]/4 * 1 = p

=> 26(0.025*(10^(-3)²) * 11/14) ohm/m = p

=> 5.1 * 10^(-6)/ ohm/m = p

Or, 0.51 * 10^(-2)

Answer 2

Explanation:

r = radius, d = diameter, p = resistivity.

R = resistance , A = area, l = length

Here,

Area of wire = πr² = π(d/2)² = π(d²/4)

= d²π/4

we know,

=> R = p(l/A)

=> R(A/l) = p

=> R(A)(1/l) = p

=> 26(d²π/4)(1/1) = p

=> 26[0.5²mm² * 22/7]/4 * 1 = p

=> 26(0.025*(10^(-3)²) * 11/14) ohm/m = p

=> 5.1 * 10^(-6)/ ohm/m = p

Or, 0.51 * 10^(-2)

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