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

Answer:

Length, L = 3 m

Area of cross section, A=1.7 \times 10^{-6} \ m^{2}A=1.7×10

−6

m

2

Resistance, R=3 \times 10^{-2} \ \text{ohm}R=3×10

−2

ohm

Solution:

We have to write the formula for resistivity of wire and mention its unit and have to calculate the resistivity of the wire

a) R=\frac{\rho L}{A}R=

A

ρL

Where,

\rhoρ is resistivity

So,

\rho=\frac{R A}{L}ρ=

L

RA

The unit is ohm meter.

b) To find the resistivity of the wire use the above formula and substitute the given values in the formula

Hence, we get,

\rho=\frac{\left(3 \times 10^{-2} \times 1.7 \times 10^{-6}\right)}{3}ρ=

3

(3×10

−2

×1.7×10

−6

)

Hence, the resistivity,

\rho=1.7 \times 10^{-8} \ \text { ohm } mρ=1.7×10

−8

ohm m

Answer 2

Given :-

• length of the wise = 3m
• area of cross-section = 1.7 × 10^-6 m²
• resistance,R = 3 × 10^-2 ohm

Solution :-

★ resistivity : The specific resistance or resistivity of the conductor is numerically equal to the resistance of that conductor whose Length is 1m and area of cross - section is 1m²

it is represent by symbol ρ called Rho

$\boxed{\bold{resistivity,ρ = \frac{RA}{L} }}$

where

• R = Resistance
• L = Length
• A = Area of cross - section

and It's SI unit is Ohm.metre

__________________________

now,

$\bold{ ρ = \frac{ \cancel{3} \times {10}^{ - 2} \times 1.7 \times {10}^{ - 6} }{ \cancel{3}} } \\ \\ \bold{: \implies 1.7 \times {10}^{ - 2} \times {10}^{ - 6} } \: \: \: \: \\ \\ \bold{: \implies1.7 \times {10}^{ - 8} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence, resistivity of the wire is 1.7 × 10^-8 ohm.m