The resistance of a wire is given by 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.

Given that the wires X and Y are made of the same material and have equal length, the resistivity and length factors in the formula will be the same for both, so we can focus on the area factor.

The cross-sectional area of a wire (which is cylindrical) is given by the formula A = π(d/2)^2, where d is the diameter of the wire.

Since the diameter of wire X is twice that of wire Y, we can say that d_X = 2d_Y.

Substituting this into the area formula gives us A_X = π(2d_Y/2)^2 = πd_Y^2 = 4A_Y.

So, the area of wire X is four times that of wire Y.

Substituting this into the resistance formula gives us R_X = ρL/A_X = ρL/(4A_Y) = R_Y/4.

So, the resistance of wire X is one fourth that of wire Y.

Question

The resistance of a wire is given by 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.

Given that the wires X and Y are made of the same material and have equal length, the resistivity and length factors in the formula will be the same for both, so we can focus on the area factor.

The cross-sectional area of a wire (which is cylindrical) is given by the formula A = π(d/2)^2, where d is the diameter of the wire.

Since the diameter of wire X is twice that of wire Y, we can say that d_X = 2d_Y.

Substituting this into the area formula gives us A_X = π(2d_Y/2)^2 = πd_Y^2 = 4A_Y.

So, the area of wire X is four times that of wire Y.

Substituting this into the resistance formula gives us R_X = ρL/A_X = ρL/(4A_Y) = R_Y/4.

So, the resistance of wire X is one fourth that of wire Y.

Knowee AI · Accepted Answer

The resistance of a wire is given by 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.

Given that the wires X and Y are made of the same material and have equal length, the resistivity and length factors in the formula will be the same for both, so we can focus on the area factor.

The cross-sectional area of a wire (which is cylindrical) is given by the formula A = π(d/2)^2, where d is the diameter of the wire.

Since the diameter of wire X is twice that of wire Y, we can say that d_X = 2d_Y.

Substituting this into the area formula gives us A_X = π(2d_Y/2)^2 = πd_Y^2 = 4A_Y.

So, the area of wire X is four times that of wire Y.

Substituting this into the resistance formula gives us R_X = ρL/A_X = ρL/(4A_Y) = R_Y/4.

So, the resistance of wire X is one fourth that of wire Y.

Two wires, X and Y , are made of the same material and have equal length. The diameterof X is twice that of Y.What is resistance of Xresistance of Y

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