The figure below represents a section of a circular conductor of nonuniform diameter carrying a current of I = 5.50 A. The radius of cross-section A₁ is r₁ = 0.270 cm. A₁ I (a) What is the magnitude of the current density across A₁? A/m² The radius ₂ at A₂ is larger than the radius ₁ at A₁. (b) Is the current at A₂ larger, smaller, or the same? O The current is larger. O The current is smaller. O The current is the same. (c) Is the current density at A₂ larger, smaller, or the same? O The current density is larger. O The current density is smaller. O The current density is the same. Assume A₂ = 24₁. (d) Specify the radius at A₂. mm (e) Specify the current at A₂. A (f) Specify the current density at A₂. A/m²
The figure below represents a section of a circular conductor of nonuniform diameter carrying a current of I = 5.50 A. The radius of cross-section A₁ is r₁ = 0.270 cm. A₁ I (a) What is the magnitude of the current density across A₁? A/m² The radius ₂ at A₂ is larger than the radius ₁ at A₁. (b) Is the current at A₂ larger, smaller, or the same? O The current is larger. O The current is smaller. O The current is the same. (c) Is the current density at A₂ larger, smaller, or the same? O The current density is larger. O The current density is smaller. O The current density is the same. Assume A₂ = 24₁. (d) Specify the radius at A₂. mm (e) Specify the current at A₂. A (f) Specify the current density at A₂. A/m²
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 <!-- Insert appropriate diagram URL here -->
### Questions
#### (a) What is the magnitude of the current density across \( A_1 \)?
\[ \text{Current Density} = \quad \underline{\hspace{100px}} \quad \text{A/m}^2 \]
#### Explanation:
To find the current density \( J_1 \) at cross-section \( A_1 \):
\[ J_1 = \frac{I}{A_1} \]
where \( A_1 \) is the area of cross-section \( A_1 \).
#### The radius \( r_2 \) at \( A_2 \) is larger than the radius \( r_1 \) at \( A_1 \)
### Questions:
#### (b) Is the current at \( A_2 \) larger, smaller, or the same?
- \( \circ \) The current is larger.
- \( \circ \) The current is smaller.
- \( \circ \) The current is the same.
Explanation:
The current \( I \) remains the same throughout a conductor under steady-state conditions. Hence, the current at \( A_2 \) is the same as at \( A_1 \).
#### (c) Is the current density at \( A_2 \) larger, smaller, or the same?
- \( \circ \) The current density is larger.
- \( \circ \) The current density is smaller.
- \( \circ \) The current density is the same.
Explanation:
The current density will vary with the cross-sectional area. Since \( r_2 \) is larger, the area \( A_2 \) is larger than \( A_1 \), so the current density \( J_2 \) will be smaller.
#### Assume \( A_2 = 2A_1 \)
#### (d) Specify the radius at \( A_2 \):
\[ \quad \underline{\hspace{100px}} \quad \text{mm} \]
#### Explanation:
Given \( A_2 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F800a48ac-05a9-41c6-9b96-1b31e1f3fea8%2Fd9ba6f16-759c-4470-acc0-3ac26acb3591%2F3vbc5h_processed.png&w=3840&q=75)
Transcribed Image Text:### Circular Conductor with Nonuniform Diameter Carrying Current
The figure below represents a section of a circular conductor of nonuniform diameter through which a current of \( I = 5.50 \) A flows. The radius of cross-section \( A_1 \) is \( r_1 = 0.270 \) cm.
 <!-- Insert appropriate diagram URL here -->
### Questions
#### (a) What is the magnitude of the current density across \( A_1 \)?
\[ \text{Current Density} = \quad \underline{\hspace{100px}} \quad \text{A/m}^2 \]
#### Explanation:
To find the current density \( J_1 \) at cross-section \( A_1 \):
\[ J_1 = \frac{I}{A_1} \]
where \( A_1 \) is the area of cross-section \( A_1 \).
#### The radius \( r_2 \) at \( A_2 \) is larger than the radius \( r_1 \) at \( A_1 \)
### Questions:
#### (b) Is the current at \( A_2 \) larger, smaller, or the same?
- \( \circ \) The current is larger.
- \( \circ \) The current is smaller.
- \( \circ \) The current is the same.
Explanation:
The current \( I \) remains the same throughout a conductor under steady-state conditions. Hence, the current at \( A_2 \) is the same as at \( A_1 \).
#### (c) Is the current density at \( A_2 \) larger, smaller, or the same?
- \( \circ \) The current density is larger.
- \( \circ \) The current density is smaller.
- \( \circ \) The current density is the same.
Explanation:
The current density will vary with the cross-sectional area. Since \( r_2 \) is larger, the area \( A_2 \) is larger than \( A_1 \), so the current density \( J_2 \) will be smaller.
#### Assume \( A_2 = 2A_1 \)
#### (d) Specify the radius at \( A_2 \):
\[ \quad \underline{\hspace{100px}} \quad \text{mm} \]
#### Explanation:
Given \( A_2 =
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