To find the resistivity of the wire, we will follow these steps:
### Step 1: Calculate the Resistance (R)
Using Ohm's Law, the resistance \( R \) can be calculated using the formula:
\[
R = \frac{V}{I}
\]
Where:
- \( V = 100.0 \, \text{V} \)
- \( I = 10.0 \, \text{A} \)
Substituting the values:
\[
R = \frac{100.0 \, \text{V}}{10.0 \, \text{A}} = 10.0 \, \Omega
\]
### Step 2: Convert Length to Meters
The length of the wire is given as \( 31.4 \, \text{cm} \). We need to convert this to meters:
\[
L = 31.4 \, \text{cm} = 31.4 \times 10^{-2} \, \text{m} = 0.314 \, \text{m}
\]
### Step 3: Calculate the Cross-sectional Area (A)
The diameter of the wire is given as \( 2.00 \, \text{mm} \). We need to convert this to meters:
\[
d = 2.00 \, \text{mm} = 2.00 \times 10^{-3} \, \text{m}
\]
The area \( A \) of the wire can be calculated using the formula for the area of a circle:
\[
A = \frac{\pi d^2}{4}
\]
Substituting \( \pi = 3.14 \) and \( d = 2.00 \times 10^{-3} \, \text{m} \):
\[
A = \frac{3.14 \times (2.00 \times 10^{-3})^2}{4}
\]
Calculating \( (2.00 \times 10^{-3})^2 \):
\[
(2.00 \times 10^{-3})^2 = 4.00 \times 10^{-6}
\]
Now substituting back into the area formula:
\[
A = \frac{3.14 \times 4.00 \times 10^{-6}}{4} = 3.14 \times 10^{-6} \, \text{m}^2
\]
### Step 4: Calculate the Resistivity (ρ)
Using the formula for resistivity:
\[
\rho = R \cdot \frac{A}{L}
\]
Substituting the values we have:
\[
\rho = 10.0 \, \Omega \cdot \frac{3.14 \times 10^{-6} \, \text{m}^2}{0.314 \, \text{m}}
\]
Calculating \( \frac{3.14 \times 10^{-6}}{0.314} \):
\[
\frac{3.14 \times 10^{-6}}{0.314} = 1.00 \times 10^{-5}
\]
Now substituting this back into the resistivity formula:
\[
\rho = 10.0 \cdot 1.00 \times 10^{-5} = 1.00 \times 10^{-4} \, \Omega \cdot \text{m}
\]
### Final Answer
The resistivity of the wire is:
\[
\rho = 1.00 \times 10^{-4} \, \Omega \cdot \text{m}
\]
