How resistivty of conductor vary if area is halved,length is double,area is double
To understand how the resistivity of a conductor varies with changes in its dimensions, we need to consider the relationship between resistance, resistivity, and the geometric properties of the conductor.
Resistance (R) is directly proportional to the resistivity of the material (ρ), length (L), and inversely proportional to the cross-sectional area (A) of the conductor. Mathematically, we have the following equation:
R = (ρ * L) / A
Now let's analyze the scenarios you mentioned:
1. If the area is halved:
If the cross-sectional area (A) of the conductor is halved, according to the formula above, the resistance (R) will double (assuming all other parameters remain constant). This is because resistance is inversely proportional to the area.
2. If the length is doubled:
If the length (L) of the conductor is doubled, again assuming all other parameters are constant, the resistance (R) will double as well. This is because resistance is directly proportional to length.
3. If the area is doubled:
If the cross-sectional area (A) of the conductor is doubled, the resistance (R) will be halved. This is because resistance is inversely proportional to the area.
In summary, the resistivity of the conductor itself remains constant, but changes in its dimensions can affect the resistance. Halving the area or doubling the length of the conductor will increase the resistance, while doubling the area will decrease the resistance.