Most telephone cables are made of copper wire of either 24 or 26 gauge. If the resistance of 24-gauge wire is 137 Ω/mile and the resistance

Question

Most telephone cables are made of copper wire of either 24 or 26 gauge. If the resistance of 24-gauge wire is 137 Ω/mile and the resistance of 26-gauge wire is 220 Ω/mile, what is the ratio of the diameter of 24-gauge wire to that of 26-gauge wire?

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Adela 3 years 2021-08-21T19:04:57+00:00 2 Answers 32 views 0

Answers ( )

  1. Xavia
    0
    2021-08-21T19:06:17+00:00
    Reply

    Answer:

    Explanation:

    Given that,

    Gauge of copper is 24 or 26

    The resistance of a wire is given as

    R=ρl/A

    Where R is resistance on ohms

    ρ is resistivity in ohm•m

    L is length of wire in m

    A is area of cross sectional area m²

    R/l = ρ/A

    First wire

    24 gauge wire has a R/l of 137Ω/mile

    Second wire

    26gauge wire has a R/l of 220Ω/mile

    Both material are made of copper and they both have the same resistivity

    R/l = ρ/A

    Then,

    ρ=RA/l

    for 24 gauge

    ρ=137A’

    A’ means area of 24 gauge wire

    For 26 gauge

    ρ=220A”

    A” means area of 26 gauge wire.

    So, the resistivity are equal

    Also, the cross section area is given as πr²= πd²/4

    Resistivity 24 =Resistivity gauge 26

    137A’=220A”

    The ratio of diameter gauge 24 to 26 is what we want

    137•πd’²/4 =220•πd”²/4

    Then,

    137•d’² =220•d”²

    d’²/d”²=220/137

    d’²/d”²=1.60584

    Take square of both sides

    d’/d”=1.267

    the ratio of the diameter of 24-gauge wire to that of 26-gauge wire is 1.27 to 3s.f

  2. thanhha
    0
    2021-08-21T19:06:26+00:00
    Reply

    Answer:

    Explanation:

    Given that,

    Gauge of copper is 24 or 26

    The resistance of a wire is given as

    R=ρl/A

    Where R is resistance on ohms

    ρ is resistivity in ohm•m

    L is length of wire in m

    A is area of cross sectional area m²

    R/l = ρ/A

    First wire

    24 gauge wire has a R/l of 137Ω/mile

    Second wire

    26gauge wire has a R/l of 220Ω/mile

    Both material are made of copper and they both have the same resistivity

    R/l = ρ/A

    Then,

    ρ=RA/l

    for 24 gauge

    ρ=137A’

    A’ means area of 24 gauge wire

    For 26 gauge

    ρ=220A”

    A” means area of 26 gauge wire.

    So, the resistivity are equal

    Also, the cross section area is given as πr²= πd²/4

    Resistivity 24 =Resistivity gauge 26

    137A’=220A”

    The ratio of diameter gauge 24 to 26 is what we want

    137•πd’²/4 =220•πd”²/4

    Then,

    137•d’² =220•d”²

    d’²/d”²=220/137

    d’²/d”²=1.60584

    Take square of both sides

    d’/d”=1.267

    the ratio of the diameter of 24-gauge wire to that of 26-gauge wire is 1.27 to 3s.f

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