**Physics Problem on Electrical Resistance and Temperature Effects****Problem Statement:**2) a) A 40-m length of copper wire at 20°C has a diameter of 0.3 mm. If a potential difference of 10 V is applied across the length of the wire, determine the current in the wire.b) If the wire is heated to 40°C while the 10-V potential is maintained, what is the resulting current in the wire?---### Analysis:This problem consists of two parts:1. Calculating the current in a copper wire given its physical dimensions and an applied voltage at a standard temperature (20°C).2. Determining the resulting current when the wire is heated to a higher temperature (40°C) while maintaining the same applied voltage.### Detailed Steps:#### Part a) Calculation at 20°C:1. **Determine the resistance (R) of the copper wire at 20°C**: - Use the resistivity formula for a conductor: \[ R = \rho \frac{L}{A} \] where: - \( \rho \) is the resistivity of copper at 20°C (typically around 1.68 x 10^-8 Ω·m). - \( L \) is the length of the wire (40 m). - \( A \) is the cross-sectional area of the wire (\( A = \pi (\frac{d}{2})^2 \)). - \( d \) is the diameter of the wire (0.3 mm or 0.0003 m).2. **Calculate the current (I) using Ohm's law**: - Ohm’s law: \( I = \frac{V}{R} \) - Where \( V \) is the potential difference (10 V).#### Part b) Calculation at 40°C:1. **Adjust the resistivity for temperature change**: - Copper's resistivity changes with temperature. This can be found using: \[ \rho_T = \rho_0 [1 + \alpha (T - T_0)] \] where: - \( \rho_T \) is the resistivity at temperature \( T \). - \( \rho_0 \) is the resistivity at the reference temperature \( T_0 \) (20°C). - \( \alpha \) is the temperature coefficient of

length of wire l =40 m diameter of wire d =0.3 mm = 0.3 x 10-3 m radius of wire r = d/2 = 0.15 x…

2) a) A 40-m length of copper wire at 20 deg c has a diameter of 0.3 mm. If a potential difference of 10 V is applied accross the length of the wire, determine the current in the wire b) If the wire is heated to 40 deg C while the 10-V potential is maintained, what is the resulting current in the wire?

2) a) A 40-m length of copper wire at 20 deg c has a diameter of 0.3 mm. If a potential difference of 10 V is applied accross the length of the wire, determine the current in the wire b) If the wire is heated to 40 deg C while the 10-V potential is maintained, what is the resulting current in the wire?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Physics Problem on Electrical Resistance and Temperature Effects**

**Problem Statement:**

2)
a) A 40-m length of copper wire at 20°C has a diameter of 0.3 mm. If a potential difference of 10 V is applied across the length of the wire, determine the current in the wire.

b) If the wire is heated to 40°C while the 10-V potential is maintained, what is the resulting current in the wire?

---

### Analysis:

This problem consists of two parts:

1. Calculating the current in a copper wire given its physical dimensions and an applied voltage at a standard temperature (20°C).
2. Determining the resulting current when the wire is heated to a higher temperature (40°C) while maintaining the same applied voltage.

### Detailed Steps:

#### Part a) Calculation at 20°C:

1. **Determine the resistance (R) of the copper wire at 20°C**:
- Use the resistivity formula for a conductor:
\[ R = \rho \frac{L}{A} \]
where:
- \( \rho \) is the resistivity of copper at 20°C (typically around 1.68 x 10^-8 Ω·m).
- \( L \) is the length of the wire (40 m).
- \( A \) is the cross-sectional area of the wire (\( A = \pi (\frac{d}{2})^2 \)).
- \( d \) is the diameter of the wire (0.3 mm or 0.0003 m).

2. **Calculate the current (I) using Ohm's law**:
- Ohm’s law: \( I = \frac{V}{R} \)
- Where \( V \) is the potential difference (10 V).

#### Part b) Calculation at 40°C:

1. **Adjust the resistivity for temperature change**:
- Copper's resistivity changes with temperature. This can be found using:
\[ \rho_T = \rho_0 [1 + \alpha (T - T_0)] \]
where:
- \( \rho_T \) is the resistivity at temperature \( T \).
- \( \rho_0 \) is the resistivity at the reference temperature \( T_0 \) (20°C).
- \( \alpha \) is the temperature coefficient of

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