Question

Determine the ratio of the resistances of two wires that are identical except that wire A is twice as long as wire B.

a) (1:2)
b) (2:1)
c) (1:4)
d) (4:1)

Answer 1

The ratio of the resistances of two wires, one twice as long as the other, is 2:1.

Step-by-step explanation:

The ratio of the resistances of two wires can be determined using the formula R = ρL/A, where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire. If wire A is twice as long as wire B, then the length of wire A is 2L and the length of wire B is L. Assuming the wires are made of the same material, the resistivities are the same. The cross-sectional area of wire A is A and the cross-sectional area of wire B is also A, since the wires are identical. Plugging these values into the formula, we get:

RA = ρ(2L)/A = 2(ρL)/A = 2(1) = 2

RB = ρL/A = 1(1) = 1

Therefore, the ratio of the resistances is 2:1, which corresponds to option (b).