The resistance (R) of a wire is inversely proportional to its cross-sectional area (A). This relationship is expressed by the formula:

R = ρL/A

where:
- R is the resistance,
- ρ (rho) is the resistivity of the material,
- L is the length of the wire,
- A is the cross-sectional area of the wire.

The cross-sectional area (A) of a wire can be calculated using the formula for the area of a circle (since the cross-section of a wire is a circle), which is:

A = π(d/2)^2

where:
- d is the diameter of the wire.

Substituting the second equation into the first gives:

R = ρL/(π(d/2)^2)

So, the resistance of a wire is inversely proportional to the square of its diameter. If the diameter of the wire is doubled, the resistance will be reduced by a factor of four (assuming the length and the material of the wire remain constant).

Question

The resistance (R) of a wire is inversely proportional to its cross-sectional area (A). This relationship is expressed by the formula:

R = ρL/A

where:
- R is the resistance,
- ρ (rho) is the resistivity of the material,
- L is the length of the wire,
- A is the cross-sectional area of the wire.

The cross-sectional area (A) of a wire can be calculated using the formula for the area of a circle (since the cross-section of a wire is a circle), which is:

A = π(d/2)^2

where:
- d is the diameter of the wire.

Substituting the second equation into the first gives:

R = ρL/(π(d/2)^2)

So, the resistance of a wire is inversely proportional to the square of its diameter. If the diameter of the wire is doubled, the resistance will be reduced by a factor of four (assuming the length and the material of the wire remain constant).

Knowee AI · Accepted Answer

The resistance (R) of a wire is inversely proportional to its cross-sectional area (A). This relationship is expressed by the formula:

R = ρL/A

where:
- R is the resistance,
- ρ (rho) is the resistivity of the material,
- L is the length of the wire,
- A is the cross-sectional area of the wire.

The cross-sectional area (A) of a wire can be calculated using the formula for the area of a circle (since the cross-section of a wire is a circle), which is:

A = π(d/2)^2

where:
- d is the diameter of the wire.

Substituting the second equation into the first gives:

R = ρL/(π(d/2)^2)

So, the resistance of a wire is inversely proportional to the square of its diameter. If the diameter of the wire is doubled, the resistance will be reduced by a factor of four (assuming the length and the material of the wire remain constant).

How is the resistance R, of a wire related to its diameter, d?

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