**Problem:**An aluminum wire has a resistance of 5.50 Ω at 10.0°C. Determine its resistance (in Ω) at 410°C. The temperature coefficient of resistivity for aluminum wire is 3.90 × 10⁻³ (°C)⁻¹. (Assume that the temperature coefficient of resistivity was measured using the reference temperature 20°C.)**Solution:**Resistance calculation box: \[ \text{8.58} \, \Omega \]**Explanation:**This problem involves calculating the change in resistance of an aluminum wire as temperature changes. The temperature coefficient of resistivity (\(\alpha\)) allows us to determine how much the resistance of a material will increase per degree change in temperature.**Formula for calculation:**\[ R_t = R_0 \cdot (1 + \alpha \cdot (T - T_0)) \]Where:- \(R_t\) is the resistance at temperature \(T\).- \(R_0\) is the original resistance (5.50 Ω at 10.0°C).- \(\alpha\) is the temperature coefficient of resistivity for aluminum (3.90 × 10⁻³ (°C)⁻¹).- \(T\) is the new temperature (410°C).- \(T_0\) is the initial temperature (10.0°C).**Calculation:**\[ R_t = 5.50 \, \Omega \times (1 + 3.90 \times 10^{-3} \times (410 - 10)) \]\[ R_t = 5.50 \, \Omega \times (1 + 3.90 \times 10^{-3} \times 400) \]\[ R_t = 5.50 \, \Omega \times (1 + 1.56) \]\[ R_t = 5.50 \, \Omega \times 2.56 \]\[ R_t \approx 14.08 \, \Omega \]Therefore, the resistance at 410°C is approximately 14.08 Ω. The incorrect value shown in the problem is 8.58 Ω.

Answered: Image /qna-images/answer/b95866f8-8c89-4925-9c97-392baa7ae83e.jpg

An aluminum wire has a resistance of 5.50 Q at 10.0°C. Determine its resistance (in Q) at 410°C. The temperature coefficient of resistivity for aluminum wire is 3.90 x 10¬3 (°C)-'. (Assume that the temperature coefficient of resistivity was measured using the reference temperature 20°C.) 8.58

An aluminum wire has a resistance of 5.50 Q at 10.0°C. Determine its resistance (in Q) at 410°C. The temperature coefficient of resistivity for aluminum wire is 3.90 x 10¬3 (°C)-'. (Assume that the temperature coefficient of resistivity was measured using the reference temperature 20°C.) 8.58

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)...

See similar textbooks

Similar questions

Given that copper's temperature coefficient of resistivity is about 3.9 x 10-3 °C-!, to what temperature must you raise a copper wire originally at 18.9 °C in order to double its resistance? Neglect any changes in dimensions. temperature: °C Does this happen in household wiring under ordinary circumstances? yes O no
option(s) will result in -2 marks. 6. The resistance of a copper wire is given by R = R, (1 + a(0 – 20)] where R, = (4.00 + 0.01)2 is the resistance of wire at 0 = 20°C. The value of resistance coefficient of copper is %3D %3D (4 x 10-3+ 1 x 10-4)/°C. It is connected with a battery of emf (10.0 + 0.1) V. (A) The resistance R at 0 = 25°C is (4.08 + 0.02)N (B) The resistance R at 0 = 50°C is (4.48 ± 0.03)N (C) The percentage error in calculation of power loss in resistance at 0 = 25°C is 3% (D) The percentage error in calculation of power loss in resistance at 0 = 50°C is 4% Space for Rough Work
In household wiring, copper wire 2.05 mm in diameter is uiten used. Find the resistance of a 35.0 m long wire. Specific resistance of copper is 1.72x 10-8 Q-m. 1
00-gauge copper wire has a diameter of 9.266 mm. Calculate the power loss in a kilometer of such wire when it carries 1.00×102 A .
A light bulb filament is made of tungsten wire with a resistivity, at room temperature (20°C), of 5.6 x 10-8 Q.m and a temperature coefficient of 0.0045 (°C)-1 The wire is 50 cm long and has a diameter of 45 Um. (a) What is the resistance of the filament at room temperature (20°C)? (Put this answer in the box) (b) What is the resistance of the filament at a typical operating temperature of 3000°C ? Answer:
A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance when heated separately. (pA-2.82 x 10 ohm.m -8 -3 -6 = 3.9 x 10 /°C; Phichrome = 2.50 x 10 m AI -3 =0.40 x 10/ °C.) The ratio of the temperature change of the nichrome wire to thetemperature change of ;a nichrome the aluminum wire is Select one: а. 10 b. 0.1 c. 9.75 d. 1
An iron wire has a resistance of 2.50 N at 33.0°C. Determine its resistance (in 2) at 433°C. The temperature coefficient of resistivity for iron wire is 5.00 × 10-3 (°C)-1. (Assume that the temperature coefficient of resistivity was measured using the reference temperature 20°C.)
A certain material has a resistance of 150 22 at 20°C. The material is then heated to 800°C, calculate the new resistance. Given the temperature coefficient of resistivity of the material is 3.65x10.³ °C-¹.
A silver wire has a resistance of 7.00 at 10.0°C. Determine its resistance (in 02) at 410°C. The temperature coefficient of resistivity for silver wire is 3.80 x 10-3 (°C)-¹. (Assume that the temperature coefficient of resistivity was measured using the reference temperature 20°C.) Q
the temperature coeficcient of resistivity of platinum is 3.9*10^-3 degrees celcius. If a platinum wire has a resistance of R0 at room temperature (23degrees), to what temperature must it be cooled in order to halve its resistance