Question

Consider two copper wires. One has twice the length and twice the cross-sectional area of the other. How do the resistances of these two wires compare? A) Both wires have the same resistance. B) The shorter wire has twice the resistance of the longer wire. The longer wire has twice the resistance of the shorter wire. D) The longer wire has four times the resistance of the shorter wire. E) The shorter wire has four times the resistance of the longer wire.

Answer 1

Answer:

option (a)

Explanation:

Wire 1:

length = 2L

Area = 2 A

Wire 2: length = L

Area = A

As we know that the resistance of a wire is directly proportional to the length of the wire and inversely proportional to the area of crossection of the wire.

Let ρ be the resistivity of the cooper wire.

Resistance of wire 1

R1 = ρ x 2L / 2 A = ρ L / A

Resistance of wire 2:

R2 = ρ x L /  A = ρ L / A

As R1 = R2

It means both the wires have same resistance.