Ratio of resistances of two copper wires X and Y

In order to find the ratio of resistances of two copper wires X and Y, we need to consider the formula for resistance:

Resistance (R) = resistivity (ρ) x length (L) / cross-sectional area (A)

The resistivity of copper is a constant value, so we can assume it to be the same for both wires.

Let's consider wire X and wire Y separately and calculate their resistances.

Wire X:
Length of wire X = 30cm = 0.3m
Radius of wire X = 2cm = 0.02m

Now, we need to calculate the cross-sectional area of wire X using the formula:

Area (A) = π x radius^2

Area of wire X = π x (0.02m)^2 = 0.0012566 m^2

Using the resistance formula, we can calculate the resistance of wire X:

Resistance of wire X = resistivity x length / area
= ρ x 0.3m / 0.0012566 m^2

Wire Y:
Length of wire Y = 10cm = 0.1m
Radius of wire Y = 1cm = 0.01m

Similarly, we can calculate the cross-sectional area of wire Y:

Area of wire Y = π x (0.01m)^2 = 0.00031416 m^2

Using the resistance formula, we can calculate the resistance of wire Y:

Resistance of wire Y = resistivity x length / area
= ρ x 0.1m / 0.00031416 m^2

Ratio of resistances:
Now, we can find the ratio of resistances of wire X and wire Y by dividing the resistance of wire X by the resistance of wire Y:

Ratio of resistances = (ρ x 0.3m / 0.0012566 m^2) / (ρ x 0.1m / 0.00031416 m^2)
= (0.3m / 0.0012566 m^2) / (0.1m / 0.00031416 m^2)
= (0.3m x 0.00031416 m^2) / (0.1m x 0.0012566 m^2)
= 0.000094248 / 0.00012566
= 0.75

Therefore, the ratio of resistances of wire X and wire Y is 0.75.

Explanation:
The resistance of a wire depends on its length, cross-sectional area, and the resistivity of the material. In this case, we have two copper wires with different lengths and radii. By using the resistance formula and calculating the resistances of both wires, we can find the ratio of resistances.

Wire X has a length of 30cm and a radius of 2cm, while wire Y has a length of 10cm and a radius of 1cm. Using the resistance formula, we can calculate the resistances of both wires. Dividing the resistance of wire X by the resistance of wire Y gives us the ratio of resist