Question

A wire is 1.1 m long and 0.91 mm in cross-sectional area. It carries a current of 4.4 A when a 1.8 V potential difference is applied between its ends. Calculate the conductivity of the material of which this wire is made. Number Units The number of significant digits is set to 2; the tolerance is +/-2%

Answer 1

To calculate the conductivity of the wire, we can use the formulas for current density and electric field. By calculating the current density using the wire's cross-sectional area and the current, and calculating the electric field using the potential difference and length, we can then divide the current density by the electric field to find the conductivity. Using the given values, the conductivity is approximately 4.14 x 10^6 A/Vm.

Step-by-step explanation:

To calculate the conductivity of the material of which the wire is made, we can use the formula:

Conductivity = current density / electric field

First, we need to find the current density. The cross-sectional area of the wire is given by the equation:

A = πr²

where r is the radius of the wire. Given the diameter of the wire, we can calculate the radius as:

r = diameter / 2 = 0.91 mm / 2 = 0.455 mm = 0.000455 m

Using this radius, we can calculate the cross-sectional area:

A = π(0.000455 m)² = 6.49 x 10^-7 m²

Next, we can calculate the current density using the formula:

J = current / A

Plugging in the values:

J = 4.4 A / (6.49 x 10^-7 m²)

J = 6.78 x 10^6 A/m²

Finally, we can calculate the electric field using the formula:

E = potential difference / length

Plugging in the values:

E = 1.8 V / 1.1 m

E = 1.64 V/m

Now, we can calculate the conductivity:

Conductivity = 6.78 x 10^6 A/m² / 1.64 V/m

Conductivity = 4.14 x 10^6 A/Vm