Question

What would be the new resistance and resistivity of a circular conducting wire if its:
(a) Length is tripled
(b) Length becomes one-third of original.
(c) Cross-sectional area is doubled
(d)cross-sectional area is halved
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Answer 1

Resistance

Explanation:

The resistance of wire is given by :

$R=\rho\dfrac{l}{A}$

l is length

A is area of cross section

(a) If length is tripled, l' = 3l

New resistance,

$R'=\rho\dfrac{l'}{A}\\\\R'=\rho\dfrac{(3l)}{A}\\\\R'=3\times \dfrac{\rho l}{A}\\\\R'=3R$

(b) If length becomes one-third of original, l' = l/3

New resistance,

$R'=\rho\dfrac{l'}{A}\\\\R'=\rho\dfrac{(l/3)}{A}\\\\R'=\dfrac{1}{3}\times \dfrac{\rho l}{A}\\\\R'=\dfrac{R}{3}$

(c) If area of cross section is doubled, A' = 2 A

New resistance,

$R'=\rho\dfrac{l}{A'}\\\\R'=\rho\dfrac{l}{(2A)}\\\\R'=\dfrac{1}{2}\times \dfrac{\rho l}{A}\\\\R'=\dfrac{R}{2}$

(d) If area of cross section is halved, A' = A/2

New resistance,

$R'=\rho\dfrac{l}{A'}\\\\R'=\rho\dfrac{l}{(A/2)}\\\\R'=2\times \dfrac{\rho l}{A}\\\\R'=2R$

Resistivity is property of a material. It always remains the same always.

Hence, this is the required solution.

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Resistance

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