If the resistivity of a material is halved, what happens to the resistance of a

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Question: If the resistivity of a material is halved, what happens to the resistance of a uniform wire of that material?

Options:

Correct Answer: Halved

Solution:

Resistance is directly proportional to resistivity; halving resistivity halves the resistance.

If the resistivity of a material is halved, what happens to the resistance of a uniform wire of that material?

If the resistivity of a material is halved, what happens to the resistance of a uniform wire of that material?

Step 1: Understand that resistance (R) is a property of a material that opposes the flow of electric current.
Step 2: Know that resistivity (ρ) is a measure of how strongly a material resists the flow of electric current.
Step 3: Remember the formula for resistance: R = ρ * (L/A), where L is the length of the wire and A is the cross-sectional area.
Step 4: If the resistivity (ρ) is halved, it means that the new resistivity is ρ/2.
Step 5: Substitute the new resistivity into the resistance formula: R' = (ρ/2) * (L/A).
Step 6: Simplify the equation: R' = (1/2) * (ρ * (L/A)) = (1/2) * R.
Step 7: Conclude that if the resistivity is halved, the resistance is also halved.

Ohm's Law – Resistance is directly proportional to resistivity, length, and inversely proportional to cross-sectional area.
Resistivity – Resistivity is a material property that affects how much resistance a wire of that material will have.