P27 019

background image

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

/3L

0

= A

0

/3. The new resistance is

R =

ρL

A

=

ρ3L

0

A

0

/3

= 9

ρL

0

A

0

= 9R

0

,

where R

0

is the original resistance. Thus, R = 9(6.0 Ω) = 54 Ω.


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