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Change in Resistance due to stretching a wire

Sreshtha asked:

“A piece of wire is redrawn without any change in volume so that its radius become half the original. Compare the new resistance with the original value.”

 

Answer:

When we redraw the wire, the volume remains constant and the resistivity also remains constant. SO, the variables are

  1. area of cross section and
  2. the length

When radius becomes half, the area of cross section increases in such a way that A1l1 = A2l2. This implies that when length is halved, area of cross section is doubled.

We know that

Therefore, the new resistance becomes (1/4) th the original value.

So, R2:R1 = 1:4