two wires of same length and material have radii r and 2 r .the ratio of the specific resistance is
Answers
The relation between resistance, length , cross sectional area and specific resistance is given below:
R= p L/A, where R- Resistance, p- specific resistance , L- length , A- cross-sectional area of the wire.
For wire 1:
p1= (R1 ×A1)/ L 1--------(1)
Also for wire 2:
p2=( R2×A2) /L2------(2)
As given, L is same for both so L1=L2
Area = π r² , where r is radius of the wire
So wire 1: A1= π r² and Wire 2: A2=4 π r²
Now dividing (1) by (2) , we get:
As material same so resistance also same.
p1/p2 = (R1×A1)/ (R2×A2)
= A1/A2 = 1:4
The ratio between the two specific resistance is 1:4.
"The resistivity of a material or a subtance is the resistance of a unit volume having sides of unit length and assuming that the current flows perpendicular to the opposite faces which is also distributed consistently over them.
Resistance is relevant only to a particular measurement circuit
Specific resistace is directly proportional to radius hence the ratio of specific resistance will be 1 : 2 "