Question

A 1.4×10⁻³ V/m electric field creates a 3.0×10¹⁷ elec/s current in a 1.1-mm-diameter aluminum wire. What is the resistance of the wire?

Answer 1

The resistance of the aluminum wire is approximately 2.91×10⁻⁴ ohms.

Step-by-step explanation:

To find the resistance of the aluminum wire, we can use Ohm's law, which states that resistance (R) is equal to voltage (V) divided by current (I). In this case, the voltage is given as 1.4×10⁻³ V/m and the current is given as 3.0×10¹⁷ elec/s. We can convert the current to amperes by dividing by the number of electrons in a coulomb, which is approximately 6.24×10¹⁸ elec/C. So the current is 4.81 A.

Now we can use Ohm's law to find the resistance: R = V/I = (1.4×10⁻³ V/m)/(4.81 A) ≈ 2.91×10⁻⁴ ohms.