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The image contains multiple physics questions about the resistance, resistivity, length, and cross-sectional area of wires. These are typically solved using the formula for resistance:

\[
R = \rho \frac{L}{A}
\]

Where:
- \( R \) is the resistance (in ohms, \( \Omega \)),
- \( \rho \) is the resistivity (in ohm-meters, \( \Omega \cdot m \)),
- \( L \) is the length of the wire (in meters),
- \( A \) is the cross-sectional area (in square meters).

I'll solve each question individually using this equation.

### 1. Question:
**A wire has a resistance of 2 ohms and a cross-sectional area of 0.5 mm². If the resistivity is \( 1.68 \times 10^{-8} \, \Omega \cdot m \), what is the length of the wire?**

Given:
- \( R = 2 \, \Omega \)
- \( A = 0.5 \, \text{mm}^2 = 0.5 \times 10^{-6} \, \text{m}^2 \)
- \( \rho = 1.68 \times 10^{-8} \, \Omega \cdot m \)

We rearrange the formula to solve for \( L \):
\[
L = \frac{R \times A}{\rho}
\]

Substitute the values:
\[
L = \frac{2 \times 0.5 \times 10^{-6}}{1.68 \times 10^{-8}} \, \text{m}
\]

Let me calculate that.The length of the wire for the first question is approximately **59.52 meters**.

### 2. Question:
**A wire has a resistance of 5 ohms and a length of 10 m. If the resistivity is \( 2.82 \times 10^{-8} \, \Omega \cdot m \), what is the cross-sectional area?**

Given:
- \( R = 5 \, \Omega \)
- \( L = 10 \, m \)
- \( \rho = 2.82 \times 10^{-8} \, \Omega \cdot m \)

We rearrange the formula to solve for \( A \):
\[
A = \frac{\rho \times L}{R}
\]

Let me calculate that.The cross-sectional area of the wire for the second question is approximately **\( 5.64 \times 10^{-8} \, \text{m}^2 \)**.

### 3. Question:
**A wire has a length of 3 m, a cross-sectional area of 1 mm², and a resistance of 4 ohms. What is the resistivity of the material?**

Given:
- \( L = 3 \, m \)
- \( A = 1 \, \text{mm}^2 = 1 \times 10^{-6} \, \text{m}^2 \)
- \( R = 4 \, \Omega \)

We solve for resistivity \( \rho \):
\[
\rho = \frac{R \times A}{L}
\]

Let me calculate this.The resistivity of the material for the third question is approximately **\( 1.33 \times 10^{-6} \, \Omega \cdot m \)**.

Would you like me to continue with the remaining questions or explain anything further?

Here are 5 related questions to expand your understanding:
1. How does increasing the length of the wire affect its resistance?
2. What happens to the resistance if you increase the cross-sectional area?
3. How does resistivity differ between conductors and insulators?
4. What are the common units of resistivity, and how can they be converted?
5. How does temperature affect the resistivity of a material?

**Tip**: Always check the units in physics problems to ensure consistency across calculations!

A wire has a resistance of 2 ohms and a cross-sectional area of 0.5 mm². If the resistivity is 1.68 × 10^-8 Ω·m, what is the length of the wire?

Learn how to calculate the length of a wire given its resistance of 2 ohms, cross-sectional area of 0.5 mm², and resistivity of 1.68 × 10^-8 Ω·m using Ohm's Law. Step-by-step solution included.

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