The thickness of a copper wire is measured as 0.00036 inches. Show step by step how to convert the thickness in engineering notation with its respective prefix symbol. The resistance of a silver wire can be calculated by the following formula: Resistance (in N) = p x l/A Where p is the resistivity of the material at room temperature (20°C), I is the length of the wire in meter, and A is the cross section area of the wire in meter If the resistivity of the silver wire is 1.59x10-8 2.m, what will be the cross section area of the wire, A, if i resistance is 100 Q and the length of wire is 800 meters?
The thickness of a copper wire is measured as 0.00036 inches. Show step by step how to convert the thickness in engineering notation with its respective prefix symbol. The resistance of a silver wire can be calculated by the following formula: Resistance (in N) = p x l/A Where p is the resistivity of the material at room temperature (20°C), I is the length of the wire in meter, and A is the cross section area of the wire in meter If the resistivity of the silver wire is 1.59x10-8 2.m, what will be the cross section area of the wire, A, if i resistance is 100 Q and the length of wire is 800 meters?
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![### Copper Wire Thickness and Silver Wire Resistance Calculations
### 1. Converting Copper Wire Thickness to Engineering Notation
The thickness of a copper wire is measured as 0.00036 inches. Follow these steps to convert the thickness to engineering notation with its respective prefix symbol.
**Step-by-Step Conversion:**
1. **Identify the significant digits:** 0.00036 has two significant digits.
2. **Convert to scientific notation:** Move the decimal point to the right so that there is only one non-zero digit to the left of the decimal point.
\[
0.00036 = 3.6 \times 10^{-4}
\]
3. **Convert to engineering notation:** Engineering notation entails adjusting the exponent to be a multiple of three (i.e., ...,-9, -6, -3, 0, 3, 6, ...).
\[
3.6 \times 10^{-4} = 0.36 \times 10^{-3} = 360 \times 10^{-6}
\]
So the final result is:
\[
0.36 \text{mils} (milli-inches)
\]
### 2. Calculating the Resistance of a Silver Wire
The resistance of a silver wire can be calculated using the following formula:
\[
Resistance (in \Omega) = \rho \times \frac{l}{A}
\]
Where:
- \(\rho\) is the resistivity of the material at room temperature (20°C),
- \(l\) is the length of the wire in meters,
- \(A\) is the cross-sectional area of the wire in square meters.
**Problem Statement:**
If the resistivity of the silver wire is \(1.59 \times 10^{-8} \ \Omega \cdot m\), what will be the cross-sectional area of the wire, \(A\), if its resistance is 100 \(\Omega\) and the length of the wire is 800 meters?
**Solution Steps:**
1. **Write down the given values:**
\[
\rho = 1.59 \times 10^{-8} \ \Omega \cdot m
\]
\[
R = 100 \ \Omega
\]
\[
l = 800](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff57c5c9b-acb3-4a3d-a39b-55eeff7ee4ad%2F2f98a497-d814-41ab-894d-2d82a3caaf54%2Fdb4pmze_processed.png&w=3840&q=75)
Transcribed Image Text:### Copper Wire Thickness and Silver Wire Resistance Calculations
### 1. Converting Copper Wire Thickness to Engineering Notation
The thickness of a copper wire is measured as 0.00036 inches. Follow these steps to convert the thickness to engineering notation with its respective prefix symbol.
**Step-by-Step Conversion:**
1. **Identify the significant digits:** 0.00036 has two significant digits.
2. **Convert to scientific notation:** Move the decimal point to the right so that there is only one non-zero digit to the left of the decimal point.
\[
0.00036 = 3.6 \times 10^{-4}
\]
3. **Convert to engineering notation:** Engineering notation entails adjusting the exponent to be a multiple of three (i.e., ...,-9, -6, -3, 0, 3, 6, ...).
\[
3.6 \times 10^{-4} = 0.36 \times 10^{-3} = 360 \times 10^{-6}
\]
So the final result is:
\[
0.36 \text{mils} (milli-inches)
\]
### 2. Calculating the Resistance of a Silver Wire
The resistance of a silver wire can be calculated using the following formula:
\[
Resistance (in \Omega) = \rho \times \frac{l}{A}
\]
Where:
- \(\rho\) is the resistivity of the material at room temperature (20°C),
- \(l\) is the length of the wire in meters,
- \(A\) is the cross-sectional area of the wire in square meters.
**Problem Statement:**
If the resistivity of the silver wire is \(1.59 \times 10^{-8} \ \Omega \cdot m\), what will be the cross-sectional area of the wire, \(A\), if its resistance is 100 \(\Omega\) and the length of the wire is 800 meters?
**Solution Steps:**
1. **Write down the given values:**
\[
\rho = 1.59 \times 10^{-8} \ \Omega \cdot m
\]
\[
R = 100 \ \Omega
\]
\[
l = 800
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