Question

ہر لما
If a wire of
Resistance "R" is streched so that
doubled. Calculate the Change in
resistane?​

Answer 1

Explanation:

a wire of length L and resistance R is stretched so that its length is doubled and the area of cross-section is halved. It means, L' = 2L and A' = A/2. ... So, the new resistance becomes 4 times of the initial resistance. (2) The resistivity of a wire remains the same on changing its length and area of cross section.

Answer 2

Correct Question:

If a wire of resistance R is stretched so that the length is doubled, what is the change in the resistance?

After the wire is stretched, the volume of it remains the same.

$\boxed{\sf{Volume\:of\:a\:cylinder=\pi r^2h}}$

Here, height will be l.

$\sf{Volume\;before\;stretching=\pi r^2l}$

$\sf{Volume\;after\;stretching=\pi \times(\bold{\dfrac{1}{2} r^2})\times (2l)}$

Hence, the shear of the wire is halved.

Let's find the ratio of the two resistances.

• Resistance varies inversely as the shear.

Hence, the multiplier of resistance will be 2.

• Resistance varies directly as the length.

Hence, the multiplier of resistance will be 2.

Hence, the ratio of the two resistance will be 1:4.

→ Second resistance: 4R [First resistance: R]

Hence, the change in the resistance is 3R.