The resistivity of a metal increases slightly with increased temperature. This can be expressed as p=po [1 + a(T-To)], where To is a reference temperature, usually 20° C, and a is the temperature coefficient of resistivity. For copper, a=3.9x 10-3 °C-1. Suppose a long, thin copper wire has a resistance of 0.25 at 20°C. Part A At what temperature, in °C, will its resistance be 0.25 ? T = Submit 15. ΑΣΦ Request Answer 2 ? °C
The resistivity of a metal increases slightly with increased temperature. This can be expressed as p=po [1 + a(T-To)], where To is a reference temperature, usually 20° C, and a is the temperature coefficient of resistivity. For copper, a=3.9x 10-3 °C-1. Suppose a long, thin copper wire has a resistance of 0.25 at 20°C. Part A At what temperature, in °C, will its resistance be 0.25 ? T = Submit 15. ΑΣΦ Request Answer 2 ? °C
College Physics
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ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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![**Understanding Resistivity and Temperature Dependence**
The resistivity of a metal increases slightly with increased temperature. This relationship is expressed by the formula:
\[ \rho = \rho_0 [1 + \alpha(T - T_0)] \]
Where:
- \( \rho \) is the resistivity at temperature \( T \).
- \( \rho_0 \) is the reference resistivity at a reference temperature \( T_0 \) (usually 20°C).
- \( \alpha \) is the temperature coefficient of resistivity.
For copper, \( \alpha \) is \( 3.9 \times 10^{-3} \, \text{°C}^{-1} \).
Example Problem:
Suppose a long, thin copper wire has a resistance of 0.25 Ω at 20°C.
**Problem Statement (Part A):**
At what temperature, in °C, will its resistance be 0.25 Ω?
**Interactive Input Box:**
Users are prompted to enter the temperature \( T \) where the resistance becomes 0.25 Ω. An input field is provided for entering the temperature in °C, accompanied by interface buttons for submission and requesting the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa038fcd8-b85f-444d-975b-575b2bd8622a%2F4826469c-6a90-4cdc-8ead-452a761a72c3%2Fd752b1g_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Resistivity and Temperature Dependence**
The resistivity of a metal increases slightly with increased temperature. This relationship is expressed by the formula:
\[ \rho = \rho_0 [1 + \alpha(T - T_0)] \]
Where:
- \( \rho \) is the resistivity at temperature \( T \).
- \( \rho_0 \) is the reference resistivity at a reference temperature \( T_0 \) (usually 20°C).
- \( \alpha \) is the temperature coefficient of resistivity.
For copper, \( \alpha \) is \( 3.9 \times 10^{-3} \, \text{°C}^{-1} \).
Example Problem:
Suppose a long, thin copper wire has a resistance of 0.25 Ω at 20°C.
**Problem Statement (Part A):**
At what temperature, in °C, will its resistance be 0.25 Ω?
**Interactive Input Box:**
Users are prompted to enter the temperature \( T \) where the resistance becomes 0.25 Ω. An input field is provided for entering the temperature in °C, accompanied by interface buttons for submission and requesting the answer.
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