A 30 m long copper wire with diameter of 8.9 mm and with 59 mA (miliAmps) of current running through it. If The resistivity of copper at roo

Question

A 30 m long copper wire with diameter of 8.9 mm and with 59 mA (miliAmps) of current running through it. If The resistivity of copper at room temperature is 1.68×10-8 Ω ⋅ m, calculate the voltage drop across the wire multiplied by 10^3. (Express the answer in two decimal places).

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Gerda 5 years 2021-08-31T10:12:57+00:00 1 Answers 11 views 0

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  1. mit
    0
    2021-08-31T10:14:12+00:00
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    Answer:

    V = 0.48 [V]

    Explanation:

    We can calculate the area of the cable using the following expression:

    A=\pi *(d/2)^{2} \\A=\pi *\frac{d^{2} }{4} \\A=\pi *(8.9*10^{-3} )/4\\A= 6.22*10^{-5}[m^{2}]

    Now we can calculate the total resistance using the following equation:

    A=\frac{de*L}{R}\\ where:\\A = area [m^2]\\de = resistivity = 1.68*10^{-8}[ohm*m]\\ L = length = 30 [m]\\R = resistance [ohm]

    R=\frac{de*L}{A}\\ R = \frac{1.68*10^{-8}*30 }{6.22*10^{-5} }\\ R = 8.102*10^{-3} [ohm]

    Using the ohm law we know that the voltage is equal to the product of the current by the resistance, in this way we can calculate the voltage.

    V = I * R

    V = 0.059 * 0.008102

    V = 0.48*10^(-3) [volt] * (10^3)

    V = 0.48 [V]

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