P27_019.PDF

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Chapter 27 - 27.19

19. Since the mass and density of the material do not change, the volume remains the same. If L 0 is the

original length, L is the new length, A 0 is the original cross-sectional area, and A is the new cross-

sectional area, then L 0 A 0 = LA and A = L 0 A 0 /L = L 0 A 0 / 3 L 0 = A 0 / 3. The new resistance is

A = ρ 3 L 0

A 0 / 3 =9 ρL 0

A 0

=9 R 0 ,

where R 0 is the original resistance. Thus, R =9(6 . 0Ω)=54Ω.

R = ρL