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).

Answer 1

V = 0.48 [V]

Step-by-step explanation:

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

`A=\pi *(d/2)^(2) \\A=\pi *(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=(de*L)/(R)\\ where:\\A = area [m^2]\\de = resistivity = 1.68*10^(-8)[ohm*m]\\ L = length = 30 [m]\\R = resistance [ohm]`

`R=(de*L)/(A)\\ R = (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]