The resistance of a wire is given by the formula R = ρL/A, where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area of the wire.

If the diameter of the wire is doubled, the cross-sectional area (A) of the wire is quadrupled (since A=πr² and r is proportional to the diameter).

Therefore, if the diameter is doubled, the new resistance (R') is given by R' = ρL/(4A).

So, the resistance is quartered or reduced by 75% when the diameter is doubled, assuming the resistivity and length of the wire remain constant.

Question

The resistance of a wire is given by the formula R = ρL/A, where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area of the wire.

If the diameter of the wire is doubled, the cross-sectional area (A) of the wire is quadrupled (since A=πr² and r is proportional to the diameter).

Therefore, if the diameter is doubled, the new resistance (R') is given by R' = ρL/(4A).

So, the resistance is quartered or reduced by 75% when the diameter is doubled, assuming the resistivity and length of the wire remain constant.

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, L is the length, and A is the cross-sectional area of the wire.

If the diameter of the wire is doubled, the cross-sectional area (A) of the wire is quadrupled (since A=πr² and r is proportional to the diameter).

Therefore, if the diameter is doubled, the new resistance (R') is given by R' = ρL/(4A).

So, the resistance is quartered or reduced by 75% when the diameter is doubled, assuming the resistivity and length of the wire remain constant.

How much does the resistance change if the diameter is doubled?

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