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A long wire with a radius of 0.450 cm carries a current. The potential difference across a 3.20 m long section of this wire is 10.0 V, and the wire carries a current of 0.440 A. (a) What is the resistance (in 0) of the 3.20 m long section of wire? Ω (b) What is the resistivity (in Q- m) of the wire? Q-m Show My Work (Ontina?

A long wire with a radius of 0.450 cm carries a current. The potential difference across a 3.20 m long section of this wire is 10.0 V, and the wire carries a current of 0.440 A. (a) What is the resistance (in 0) of the 3.20 m long section of wire? Ω (b) What is the resistivity (in Q- m) of the wire? Q-m Show My Work (Ontina?

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College Physics
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### Electrical Resistance and Resistivity **Problem Statement:** A long wire with a radius of 0.450 cm carries a current. The potential difference across a 3.20 m long section of this wire is 10.0 V, and the wire carries a current of 0.440 A. **Questions:** (a) What is the resistance (in Ω) of the 3.20 m long section of the wire? - ______________ Ω (b) What is the resistivity (in Ω·m) of the wire? - ______________ Ω·m ### Instructions for Solution: 1. Calculate the resistance using Ohm’s Law: - \( V = IR \) - Where \( V \) is the potential difference, \( I \) is the current, and \( R \) is the resistance. Solve for \( R \). 2. To find resistivity, utilize the formula: - \( R = \rho \frac{L}{A} \) - Rearrange to solve for resistivity \( \rho \): - \(\rho = R \frac{A}{L}\) - Where \( L \) is the length of the wire, and \( A \) is the cross-sectional area of the wire. Find \( A \) using: - \( A = \pi r^2 \) - Where \( r \) is the radius of the wire. ### Notes: - Ensure all units are converted to SI units before calculations (e.g., convert radius to meters). - Consider significant figures based on the given data. ### Additional Help: - Click "Show My Work" for guided problem-solving steps if needed. This text provides information for an educational context on solving problems related to electrical resistance and resistivity, suitable for middle to advanced level physics students.
Transcribed Image Text:### Electrical Resistance and Resistivity **Problem Statement:** A long wire with a radius of 0.450 cm carries a current. The potential difference across a 3.20 m long section of this wire is 10.0 V, and the wire carries a current of 0.440 A. **Questions:** (a) What is the resistance (in Ω) of the 3.20 m long section of the wire? - ______________ Ω (b) What is the resistivity (in Ω·m) of the wire? - ______________ Ω·m ### Instructions for Solution: 1. Calculate the resistance using Ohm’s Law: - \( V = IR \) - Where \( V \) is the potential difference, \( I \) is the current, and \( R \) is the resistance. Solve for \( R \). 2. To find resistivity, utilize the formula: - \( R = \rho \frac{L}{A} \) - Rearrange to solve for resistivity \( \rho \): - \(\rho = R \frac{A}{L}\) - Where \( L \) is the length of the wire, and \( A \) is the cross-sectional area of the wire. Find \( A \) using: - \( A = \pi r^2 \) - Where \( r \) is the radius of the wire. ### Notes: - Ensure all units are converted to SI units before calculations (e.g., convert radius to meters). - Consider significant figures based on the given data. ### Additional Help: - Click "Show My Work" for guided problem-solving steps if needed. This text provides information for an educational context on solving problems related to electrical resistance and resistivity, suitable for middle to advanced level physics students.
Expert Solution
Step 1

Given data: 

Radius (r) = 0.450 cm = 0.450×10-2 m

Length (L) = 3.20 m

Voltage (V) = 10.0 V

Current (I) = 0.440 A

Required:

Resistance (R) and resistivity (ρ) 

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