Question

A cylindrical conductor of length 'L' and uniform area of cross section has resistance 'R' the area of a cross section of another conductor of same material and the same resistance but of length 2L
(A) A/2
(B) 3A/2
(C) 2A
(D) 3A

Answer 1

Answer:

(c)  2A

Explanation:

resistance = length/ area of cross section

let r be resistance, l length,  a area in 1st wire and a' in 2nd wire

In the 1st wire= r=l/a or a=l/r ........(i)

in the 2nd wire= r=2l/a'

                      a'= 2l/r

                      a'= 2a

Answer 2

Answer:

The resistance of a wire can be expressed as

R=ρ L/A

A=ρ R/L

where,

ρ - Resistivity - the factor in the resistance which takes into account the nature of the material is the resistivity

L - Length of the conductor

A - Area of a cross-section of the conductor.

From this relation, we observe that the length is directly proportional to the resistance and the area of cross-section is inversely proportional to the resistance.

In this case, the length of the conductor is doubled (2L) and so the resistance will be 2R. For the resistance to remain the same as R, the area of cross-section is also doubled as 2A.

Hence, the area of cross-section is 2A.

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