Question

A wire of length 3 m and area of cross-section 1.7 × 10-6 m2 has a resistance 3 × 10-2 ohm.
a. What is the formula for resistivity of the wire and what is the unit of it
b. Calculate the resistivity of the wire​

Answer 1

GIVEN :–

• Length = 3m

• Cross section area = 1.7 × $\:\: {10}^{ - 6} \:\:$m²

• Resistance = 3 × $\:\: {10}^{ - 2} \:\:$ohm

TO FIND :–

(a). What is the formula for resistivity of the wire and what is the unit of it.

(b). Calculate the resistivity of the wire .

SOLUTION :–

• We know that –

$\\ \dashrightarrow { \boxed{\bf \: R = \dfrac{ \rho \: L}{A}}}$

• Here –

$\\ \: \: { \huge{.}} \: \: \bf \: R = resistance$

$\\ \: \: { \huge{.}} \: \: \bf \: L = Length$

$\\ \: \: { \huge{.}} \: \: \bf \: A = Area$

$\\ \: \: { \huge{.}} \: \: \bf \: \rho = resistivity$

• So that –

$\\ \dashrightarrow \large { \boxed{\bf \rho = \dfrac{RA}{L}}}$

• Unit = ohm × meter

• Now put the values –

$\\ \implies {\bf \rho = \dfrac{(3 \times {10}^{ - 2}) (1.7 \times {10}^{ - 6})}{ 3}}$

$\\ \implies {\bf \rho = \dfrac{ \cancel3 \{1.7 \times {10}^{( - 6 - 2)}\}}{ \cancel3}}$

$\\ \implies \large{ \boxed {\bf \rho = 1.7 \times {10}^{ - 8} \: ohm - m}}$

$\\ \rule{220}{2}$

Answer 2

Given:

Length of wire,l= 3 m

Area of cross-section,A= 1.7 × 10⁻⁶ m²

Resistance of wire,R=  3 × 10⁻²Ω

To Find:

a) What is the formula for resistivity of the wire and what is the unit of it

b) Calculate the resistivity of the wire

Solution:

a) Resistivity ρ of a conductor is given by

$\pink{\underline{\boxed{\bf{\rho=\dfrac{RA}{l}}}}}$

where,

R is the resistance of conductor

A is area of cross-section of wire

l is length of conductor

Unit of resistivity- Ωm

b) Let the resistivity of wire ρ be

So,

$\longrightarrow\rm{\rho=\dfrac{RA}{l}}$

$\longrightarrow\rm{\rho=\dfrac{3\times10^{-2}\times1.7\times10^{-6}}{3}}$

$\longrightarrow\rm\green{\rho=1.7\times10^{-8}\ \Omega m}$

Hence, the resistivity of given wire is 1.7×10⁻⁸Ωm.