Question

what would be the new resistance and resistivity of a circular conducting wire if its:

(a)length is tripled

(b) cross sectional area is halved

(c) length becomes three fourth an d cross section becomes two third of the original

Answer 1

we know that the resistance is given as

R = ρL / A

so,

R ~ ρ

R ~ L

and

R ~ 1/A

now,

(1)

if length is tripled the new resistance will be become

R' ~ L'

[L' = 3L]

so,

R' ~ 3L

so,

R = 3R

so, the resistance will be tripled as well.

..

(2)

if the cross-sectional area is halved the new resistance will become

R' ~ 1/A'

[A' = A/2]

so,

R' ~ 1/(A/2) ~ 2/A

so,

R' = 2R

so, the new resistance will be doubled.

..

(3)

if the length becomes three-fourth and area of cross-section becomes two-thirds

R' ~ L'/A'

[L' = (3/4)L and A' = (2/3)A]

so,

R' ~ (3/4)L / (2/3)A

or

R' ~ (9/4).(L / A)

so,

R' ~ (9/4)R

so, the new resistance becomes nine-fourths its original value.