Introduction:

The resistance of a wire is influenced by several factors such as its length, cross-sectional area, and the resistivity of the material it is made of. Resistivity is a property of a material that determines its ability to resist the flow of electric current. When the material of a wire is changed to one with a resistivity three times higher, the resistance of the wire will be affected.

Explanation:

1. Definition of Resistivity:
- Resistivity is a measure of how strongly a material opposes the flow of electric current.
- It is denoted by the symbol ρ and is measured in ohm-meters (Ω.m).

2. Relationship between Resistance and Resistivity:
- The resistance of a wire can be calculated using the formula: R = (ρ * L) / A, where R is the resistance, ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.
- This formula shows that resistance is directly proportional to resistivity.

3. Effect of Changing Resistivity:
- If the resistivity of the wire's material is three times higher than before, the resistance of the wire will also increase.
- This is because resistance is directly proportional to resistivity, as explained in the previous point.
- When resistivity increases, it becomes more difficult for electric current to flow through the wire, resulting in higher resistance.

4. Mathematical Explanation:
- Let's assume the initial resistivity of the wire's material is ρ1, and the final resistivity is ρ2 (which is three times ρ1).
- Using the formula R = (ρ * L) / A, we can rewrite it as R = (ρ1 * L) / A for the initial wire and R = (ρ2 * L) / A for the wire with changed material.
- As ρ2 = 3 * ρ1, we can substitute ρ2 in the second equation: R = (3 * ρ1 * L) / A.
- Therefore, the resistance of the wire with the changed material is three times greater than the resistance of the initial wire.

Conclusion:

When the material of a wire is changed to one with a resistivity three times higher, the resistance of the wire also increases. This is due to the direct proportionality between resistance and resistivity. The resistance can be calculated using the formula R = (ρ * L) / A, where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire. By substituting the new resistivity value into the formula, it can be observed that the resistance of the wire becomes three times greater.

The resistance of wire increased three times.. becaause resistance of wire is directly proportional to the electrical resistivity of wire