How does the resistance of a Wire vary with its area of cross section? Explain?

Question

Answer

Answer

Answer

The resistance of a wire is inversely proportional to the area of cross section of the conductor. The reason behind this is that if the area of the conductor is more then the electrons present in it are more spaced out and the number of collisions between them gets decreased which results in decreased resistance to the flow of current .

Answer

Resistance of a Wire with its Area of Cross Section

Resistance of a wire is the opposition it offers to the flow of electric current through it. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. This relation is given by the formula:

R = ρL/A

where R is resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

Effect of Cross-Sectional Area on Resistance

As per the above formula, we can see that resistance is inversely proportional to the cross-sectional area of the wire. This means that if the cross-sectional area of the wire is increased, the resistance will decrease and vice versa. The reason for this can be explained by the following points:

- When the cross-sectional area of the wire is increased, the electrons have more space to move around and hence, the number of collisions between them decreases. This results in a decrease in resistance.
- On the other hand, if the cross-sectional area is decreased, the electrons get crowded and collide more frequently, increasing the resistance.

Examples

To illustrate this concept, consider a wire made of copper, which has a resistivity of 1.68 × 10^-8 Ωm. Let us assume that the length of the wire is 1 meter.

- If the cross-sectional area of the wire is 1 mm^2, the resistance of the wire would be R = (1.68 × 10^-8 Ωm × 1 m) / 1 mm^2 = 0.0168 Ω
- If the cross-sectional area of the wire is increased to 2 mm^2, the resistance of the wire would be R = (1.68 × 10^-8 Ωm × 1 m) / 2 mm^2 = 0.0084 Ω

As we can see, the resistance of the wire decreases as the cross-sectional area is increased.

Conclusion

In conclusion, the resistance of a wire is inversely proportional to its cross-sectional area. This means that the larger the cross-sectional area of the wire, the lower its resistance. This relation can be explained by the fact that electrons have more space to move around in a larger cross-sectional area, resulting in fewer collisions between them, and hence, a lower resistance.

Answer

Resistance is inversely proportional to area of cross section. larger will be the area lower will be the resistance and vice versa. this is because through a conductor with large area of cross section current can easily flow and hence resistance is low.

Answer

Resistance is equal to row × length divided by area so it is inversely proportional

Answer

Resistance of wire is inversely proportional to its area of cross section..

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