Three copper wires have lengths and cross-sectional areas of (l and A) ,(2land A / 2) and (l/2 and 2A) . Resistance will be minimum in

Options

A. wire of cross-sectional area A
B. wire of cross-sectional area A/2
C. wire of cross-sectional area 2 A
D. same in all three cases

Answer

C

Explanation

Given : Length and cross-sectional area of first wire = l and A , length and cross-sectional area of second wire = 2 l and A/2 and length and
cross-sectional area of third wire
`= l // 2 ` and 2A
We know that the resistance of a
wire (R) `=pxx(l)/(A)prop(l)/(A)`
Thus resistance of the wire will be minimum, when its length is minimum and cross-sectional area is maximum.
Since the third wire has minimum length (l/2) and maximum cross-sectional area (2A).
`:.` Resistance in this wire will be minimum .