What length of the wire (specific resistance `48 xx 10^(-8)Omega-m` ) is needed to make a resistance of `4.2Omega` ?

Options

A. 1.1m
B. 2.1m
C. 3.1m
D. 4.1m

Answer

A

Explanation

Given : Specific resistance of wire
`(p) = 48 xx 10^(-8) Omega m `,
Resistance of wire `(R) = 4.2 Omega ` and
Diameter of wire (d) = 0 . 4 mm or
Radius `(r)= 0.2 mm = 2 xx 10^(-4)` mm or
We know that area of wire
`(A) = pi r ^(2) = 3 . 14 xx ( 2 xx 10 ^(-4))^(2)`
`= 12 . 56 xx 10^(-8) m^(2)`
We also know that resistance of the
wire `(R) = p xx (L)/(A)`
or L `= (RxxA)/(p)`
` = (4.2 (12.56 xx 10^(-8)))/(48 xx 10^(-8)) = 1 . 1 ` m