A cylindrical conductor of length ‘l’ and area of cross section ‘A’ has a resistance ‘R’. Another conductor of length 2.5l and resistance 0.

Question

A cylindrical conductor of length ‘l’ and area of cross section ‘A’ has a resistance ‘R’. Another conductor of length 2.5l and resistance 0.5R of the same material has area of cross section ?

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Tryphena 4 years 2021-09-03T02:48:34+00:00 2 Answers 9 views 0

Answers ( )

  1. Nick
    0
    2021-09-03T02:49:57+00:00
    Reply

    R = (ρ x l)/A [Resistance = resisitivity times length divided by area of cross-section]

    0.5R = (ρ x 2.5l)/A’

    0.5R/2.5 = (ρ x l)/A’

    R/5 = (ρ x l)/A’

    R = 5(ρ x l)/A’

    (ρ x l)/A = 5(ρ x l)/A’

    A’ = 1/5 A

    A’ = 0.2 A

  2. thnahdat
    0
    2021-09-03T02:50:13+00:00
    Reply

    Answer: A₂ = 5A

    Explanation:

    L1 = L

    A1 = A

    R1 = R

    R2 = 0.5R

    L₂ = 2.5L

    A2 =?

    from resistance formula,

    R = ρL / A

    but since they are of the same material,

    ρ₁ = ρ₂ = ρ

    R₁ = ρL₁ / A₂ …..equation i

    R₂ = ρL₂ / A₂……equation ii

    dividing equation ii by i,

    R₂ / R₁ = (L₂ / A₂) / (L₁ / A₁)……. [ρ cancles out]

    R₂ / R₁ = (L₂ * A₁) / (A₂ * L₁)

    0.5R / R = (2.5L * A) / (A₂*L)

    0.5 = 2.5A / A₂

    A₂ = 2.5A / 0.5

    A₂ = 5A

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