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Resistance and Resistivity

Simran Asked

“Two wires A and B of equal lengths,different cross-sectional areas and made of same metal a)name the property which is same for both the wires. b)name the property which is different for both the wires”

Answer:

Since both the wires are of same metal, the resistivity will be same for both whereas since the dimensions (Area of cross section here) are different, the resistance will be different

Change in resistance due to stretching a wire

“There is a wire whose resistance is R. it is streched, and its length gets increased to 2%. find new resistance.” – Knishka Agrawal asked

Answer: The resistivity does not change due to stretching, but the length and area of cross section changes; but the volume remains constant. Therefore, resistance changes which can be calculated from the formula for Resistance

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

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