Question

Calculate the area of cross section of a wire if it's length is 1.0m ,it's resistance is 23 omega and the resistivity of the material of the wire is 1.84*10 power -6

Answer 1

Concept :-

R = (r × l)/A

where, R = resistance of a wire

r = resistivity of a wire

l = length of wire

A = area of cross-section

Solution:-

R = 23 omega

l = 10 m

r = 1.84 × 10 to power (-6)

as we know that,

R = (r × l)/A

or, A = (r × l)/R

or, A = {1.84 × (10 to power -6) × 10}/23

or,A = 8 × 10 to power (-7) m↑2

Answer 2

Solution :

$\bigstar \: \: \boxed{\sf R = \rho \dfrac{l}{A}}\: \: \bigstar$

$: \implies\sf 23 \: = \: 1.84 \: \times \: {10}^{ - 6} \: \times \: \dfrac{1}{A}$

$: \implies\sf A \: = \: \dfrac{1.84 \: \times \: {10}^{ - 6}}{23}$

$: \implies\sf A \: = \: \dfrac{184 \: \times \: {10}^{ - 8}}{23}$

$: \implies\underline{ \boxed{\sf A \: = \: 8 \: \times \: {10}^{ - 8} m^{2}}} \: \: \bigstar$

$\underline{\sf Therefore,\:the \: area \: of \: cross \: section \: of \: wire \: is \: \bf{ 8 \times 10^{-8}\:m^2}}.$