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6 October, 02:08

A long metallic wire is stretched along the x direction. The applied potential difference along

the wire is 12 volts. The resistance of the wire is estimated to be 8 Ohm.

a. Calculate the current in the wire and the passing charge in 2 seconds.

b. Calculate the electric power dissipated in the wire.

This wire has a length of 100 m and the material of the wire has a resistivity of 1.6 x 10 - 8 Ωm.

c. Calculate the cross-section area of the wire.

d. Calculate the conductivity of the wire.

e. What is the capacitance of the capacitor, that is connected to a series resistor of 8 MΩ in an RC

circuit that has a time constant of one second.

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Answers (1)
  1. 6 October, 05:51
    0
    a) I = 1.5 A, b) P = 18 W, c) A = 8 10⁻⁷ m², d) σ = 0.625 10⁸ (Ω m) ⁻¹,

    e) C = 0.125 10⁻⁶ F

    Explanation:

    a) for this exercise let's use Ohm's Law

    V = I R

    I = V / R

    I = 12/8

    I = 1.5 A

    b) the power is given by the expression

    P = V I

    P = V V / R = V² / R

    P = 12²/8

    P = 18 W

    c) the resistance of the wire is given by

    R = ρ l / A

    A = ρ l / R

    A = 1.6 10⁻⁸ 100/8

    A = 8 10⁻⁷ m²

    d) conductivity is the inverse of resistivity

    σ = 1 / ρ

    σ = 1 / 1,610⁻⁸

    σ = 0.625 10⁸ (Ω m) ⁻¹

    e) In an RC circuit the response time is

    τ = RC

    C = τ / R

    C = 1/8 10⁶

    C = 0.125 10⁻⁶ F
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