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

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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.
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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