Q.

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 ____ × 10-8 Ωm.


see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

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 is 48 × 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= d2 
On substituting the value, we get the radius as
   r= 0.42
   r=0.2 mm
   r=0.2 × 10-3 m
Also, the area of cross-section (A) is given by
     A= π r2
On substituting the given values, we get the cross-sectional area as
A=3.14 × (0.2 × 10-3)2
A=0.1256 × 10-6 m2
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 m2. Its SI unit is ohm-metre (Ωm). It depends on the nature of the substance.
So, specific resistance (ρ) is given by
     ρ= RAl
On substituting the given values, we get the specific resistance as
ρ= 4.2 ×0.1256 × 10-61.1
ρ=48 × 10-8 Ωm
Hence, the specific resistance is 48 × 10-8 Ωm.
 
Watch 3-min video & get full concept clarity
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon