AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

The specific resistance of a wire of length $1.1 m, 0.4 mm$ diameter and having a total resistance of $4.2 Ω$ is ____ $\times 10^{- 8} Ωm$ .

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The specific resistance of a wire of length

1.1 m, 0.4 mm

diameter and having a total resistance of

4.2 Ω

48 \times 10^{- 8} Ωm

.
Given,
Resistance,

R = 4.2 Ω

Length,

l = 1.1 m

Diameter,

d = 0.4 mm

Since diameter is double the radius, the radius is given by

r = \frac{d}{2}

On substituting the value, we get the radius as

\Rightarrow r = \frac{0.4}{2}

\Rightarrow r = 0.2 mm

\Rightarrow r = 0.2 \times 10^{- 3} m

Also, the area of cross-section

(A)

is given by

A = π r^{2}

On substituting the given values, we get the cross-sectional area as

\Rightarrow A = 3.14 \times {(0.2 \times 10^{- 3})}^{2}

\Rightarrow A = 0.1256 \times 10^{- 6} m^{2}

Now, it is known that the specific resistance or resistivity of a substance is numerically equal to the resistance when the substance is

1 m

long and has a cross-sectional area of

1 m^{2}

. Its SI unit is

ohm - metre (Ωm)

. It depends on the nature of the substance.
So, specific resistance

(ρ)

is given by

ρ = \frac{RA}{l}

On substituting the given values, we get the specific resistance as

\Rightarrow ρ = \frac{4.2 \times 0.1256 \times 10^{- 6}}{1.1}

\Rightarrow ρ = 48 \times 10^{- 8} Ωm

Hence, the specific resistance is

48 \times 10^{- 8} Ωm

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!