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Chapter 27: Q. 71 (page 765)

71. A long, round wire has resistanceR. What will the wire's resistance be if you stretch it to twice its initial length?

Short Answer

Expert verified

The wire's resistance, if stretch to twice its initial length, is 4R.

Step by step solution

01

Given information

A long, round wire has resistanceR. Resistance of the wire is R=ρLA,where p indicates the resistivity, L is the length and A is the cross sectional area.

02

Explanation

In the initial state of the wire will be,
R=ρLA
In elongation, the volume is the quantity that doesn't switch, but the density accomplishes. This indicates that the product of the length with the cross-section surface area is stable. To discover the area after the stretching as,
LA=L'A'⇒A'=LL'A
The resistance of the elongated wire evolves:
R'=ρL'A'=AA'L'LR

Find the ratio from previous term,
AA'=L'L

Applying,

R'=L'L2R

R'=22R

=4R.

Therefore, The wire's resistance, if stretch to twice its initial length, is4R

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