Question

If the length and diameter of a conductor is
tripped, the resistance will increase
approximatley by
(A) 66% (B) 33%
(C) - 66% (D) - 33%.​

Answer 1

Answer:

A) Decreases two times. Hint: Resistance of the conductor is directly proportional to the resistivity and length of the conductor, and inversely proportional to the area of the conductor. .

Answer 2

Explanation:

If the length and diameter of a conductor is double, then what will be its resistance?

If the conductor is the same, and thus has the same resistivity, and the conductor is cylindrical, then the resistance will halve. This is because:

R=ρLA

Where R is the resistance, ρ (the greek letter rho) is the resistivity of the material (which will remain constant if the material is kept the same, as it is a property of a material itself), and A is the cross sectional area of the conductor.

Hence, if the length is doubled, then L will increase by a factor of 2, and if the diameter is doubled, then A will increase by a factor of 4 (this is because the area of a circle (and hence the cross-sectional area of a cylinder) is A=πr2 , where A is the area and r is the radius, and if the diameter is doubled then the radius is doubled as well, and hence the area is quadrupled). This means that the resistance increased by a factor of 24 which simplifies down to 12 , meaning that resistance is halved.