An aluminum wire 2.053 mm in diameter (12-gauge) carries a current of 1.5 amps. Overall Hint a. What is the number density of charge carriers (electrons) in the wire? Hint for (a) The number density of electrons in the wire is 1 m³ (Use "E" notation to enter your answer in scientific notation. For example, to enter 3.14 × 10¹2, enter "3.14E12".) b. What is the magnitude of the drift velocity of the electrons? Hint for (b) The drift velocity of the electrons is va = m/s. c. What would be the drift velocity if the same gauge copper were used instead of aluminum? Hint for (c) For the same gauge copper wire, the drift velocity would be vd = m/s. There is a disconnect between how small drift velocities are and how quickly electrical signals travel through wires (nearly at the speed of light). For the moment, treat the two as completely unrelated to each other.
An aluminum wire 2.053 mm in diameter (12-gauge) carries a current of 1.5 amps. Overall Hint a. What is the number density of charge carriers (electrons) in the wire? Hint for (a) The number density of electrons in the wire is 1 m³ (Use "E" notation to enter your answer in scientific notation. For example, to enter 3.14 × 10¹2, enter "3.14E12".) b. What is the magnitude of the drift velocity of the electrons? Hint for (b) The drift velocity of the electrons is va = m/s. c. What would be the drift velocity if the same gauge copper were used instead of aluminum? Hint for (c) For the same gauge copper wire, the drift velocity would be vd = m/s. There is a disconnect between how small drift velocities are and how quickly electrical signals travel through wires (nearly at the speed of light). For the moment, treat the two as completely unrelated to each other.
Related questions
Question
![### Electrical Drift Velocity in Wires
**Problem Description:**
An aluminum wire with a diameter of 2.053 mm (12-gauge) carries a current of 1.5 amps.
---
**Overall Hint:**
To solve the problems outlined, utilize the principles of charge carrier density and drift velocity.
---
**Questions:**
**a. What is the number density of charge carriers (electrons) in the wire?**
- **Hint for (a):**
The number density of electrons in the wire can be calculated and entered in scientific notation format. For instance, to represent \(3.14 \times 10^{12}\), enter "3.14E12."
- **Answer Box:**
\[
\text{The number density of electrons in the wire is} \ \boxed{\phantom{3.14E12}} \ \text{m}^{-3}.
\]
---
**b. What is the magnitude of the drift velocity of the electrons?**
- **Hint for (b):**
Calculate the drift velocity based on the current and charge carrier density.
- **Answer Box:**
\[
\text{The drift velocity of the electrons is} \ v_d = \boxed{\phantom{0.0}} \ \text{m/s}.
\]
---
**c. What would be the drift velocity if the same gauge copper wire were used instead of aluminum?**
- **Hint for (c):**
Consider the differences in material properties between copper and aluminum when calculating the drift velocity.
- **Answer Box:**
\[
\text{For the same gauge copper wire, the drift velocity would be} \ v_d = \boxed{\phantom{0.0}} \ \text{m/s}.
\]
---
**Discussion:**
There is a noticeable disconnect between the small magnitude of drift velocities and the rapid speed at which electrical signals travel through wires (almost at the speed of light). For practical purposes, consider these concepts as independent of one another in this context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0edab40-1f13-4f88-959e-31b8927d437a%2F9e4b07e3-2823-4754-af96-35fb594005fe%2Fommwyy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Electrical Drift Velocity in Wires
**Problem Description:**
An aluminum wire with a diameter of 2.053 mm (12-gauge) carries a current of 1.5 amps.
---
**Overall Hint:**
To solve the problems outlined, utilize the principles of charge carrier density and drift velocity.
---
**Questions:**
**a. What is the number density of charge carriers (electrons) in the wire?**
- **Hint for (a):**
The number density of electrons in the wire can be calculated and entered in scientific notation format. For instance, to represent \(3.14 \times 10^{12}\), enter "3.14E12."
- **Answer Box:**
\[
\text{The number density of electrons in the wire is} \ \boxed{\phantom{3.14E12}} \ \text{m}^{-3}.
\]
---
**b. What is the magnitude of the drift velocity of the electrons?**
- **Hint for (b):**
Calculate the drift velocity based on the current and charge carrier density.
- **Answer Box:**
\[
\text{The drift velocity of the electrons is} \ v_d = \boxed{\phantom{0.0}} \ \text{m/s}.
\]
---
**c. What would be the drift velocity if the same gauge copper wire were used instead of aluminum?**
- **Hint for (c):**
Consider the differences in material properties between copper and aluminum when calculating the drift velocity.
- **Answer Box:**
\[
\text{For the same gauge copper wire, the drift velocity would be} \ v_d = \boxed{\phantom{0.0}} \ \text{m/s}.
\]
---
**Discussion:**
There is a noticeable disconnect between the small magnitude of drift velocities and the rapid speed at which electrical signals travel through wires (almost at the speed of light). For practical purposes, consider these concepts as independent of one another in this context.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
