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.

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

electrical to thermal

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