A material is formed into a long rod with a square cross section 0.31 cm on each side. When a 100 V voltage is applied across a 16 m length of the rod, a 4.6 A current is carried.

What is the resistivity of the material?

This is a rectangular wire rather than a cylindrical.

I use V=IR to find the resistance
and R=p L/A to find resistivity (p)

I don't know how to find croos sectional area.

Please help, thank you.

It says the cross section is square

Area of square = side^2
or in this case
.31cm*.31 cm
or
0.0031 meter * 0.0031 meter

To find the cross-sectional area of a square rod, you need to know its side length. In this case, the side length is given as 0.31 cm. To calculate the area, you need to square the side length.

The formula for the area of a square is A = side length * side length.

So, in this case, the cross-sectional area (A) of the square rod is A = 0.31 cm * 0.31 cm.

Calculating this, you get:
A = 0.0961 cm².

Now that you have the cross-sectional area, you can proceed to find the resistivity (p).

First, you have the applied voltage (V) of 100 V and the current (I) of 4.6 A.

Using Ohm's law, V = I * R, you can rearrange the formula to solve for resistance (R):

R = V / I.

Substituting the given values, you get:
R = 100 V / 4.6 A.

Calculating this, you get:
R = 21.74 Ω.

Finally, you can use the formula R = p * (L / A) to find the resistivity (p).

Rearranging the formula, you get:
p = R * (A / L).

Substituting the values, you get:
p = 21.74 Ω * (0.0961 cm² / 16 m).

Note: You need to convert the cross-sectional area from square centimeters to square meters to maintain consistent units in the calculation. 1 cm² = 0.0001 m².

Calculating this, you get:
p = 21.74 Ω * (0.000961 m² / 16 m).

Simplifying, you get:
p = 0.001305 Ω·m.

Therefore, the resistivity (p) of the material is approximately 0.001305 Ω·m.