Physics · Current Electricity · NEET
In the base formula R = ρL/A, the length L and area A are independent. If you just take a longer wire (different wire), only L changes, so R ∝ L. But when you STRETCH one wire, its volume V = A×L is fixed (same amount of metal). So A = V/L falls as L rises. Put A = V/L into R = ρL/A and you get R = ρL²/V, which means R ∝ L². The extra L comes from the area shrinking.
It decreases. The wire gets longer and thinner. Because volume is constant, if length becomes n times, area becomes 1/n times (A ∝ 1/L). The radius shrinks even faster: r ∝ 1/√L. This thinning is exactly why resistance climbs more than you might first expect.
It becomes 4R, not 2R. Doubling the length halves the area (constant volume), and R = ρL/A picks up a factor of 2 from L and another factor of 2 from 1/A. So R_new = R × 2² = 4R. The common wrong answer 2R forgets that the area also changed.
Use R ∝ 1/A² = 1/r⁴ at constant volume. Since A ∝ 1/L, resistance R ∝ L² ∝ (1/A)² ∝ 1/r⁴. So if the radius becomes half, resistance becomes 2⁴ = 16 times. Always check whether the question gives you length, area, or radius, then use the matching power.
No. Resistivity ρ depends on the material and temperature, not on shape. Stretching only changes the geometry (L and A). As long as temperature is unchanged, ρ stays the same, which is why the whole R ∝ L² result is purely geometric.
The resistance of a wire is R. If it is melted and stretched to n times its original length, its new resistance is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
At constant volume, R = ρL²/V, which means R ∝ L². If length becomes n times the original, resistance becomes n² times: R_new = n²R.
Stretching keeps volume fixed, so area A = V/L shrinks as length grows. In R = ρL/A, one factor of L comes from length and one from the smaller area, giving L².
At constant volume, R ∝ 1/r⁴. Halving the radius multiplies resistance by 2⁴ = 16, so the new resistance is 16 times the original.
No. Resistivity depends only on the material and temperature. Stretching changes shape (L and A) but not ρ, so the change in R is purely geometric.
No. A different, longer wire changes only L, giving R ∝ L. Stretching the same wire fixes volume and also thins it, giving R ∝ L². Always identify whether volume is constant.
