PoentWeptgj

2022-07-20

A resistor is made from a material that has a temperature coefficient of resistivity of $2.0\times {10}^{-3}{/}^{\circ}C$. Its resistance is $30\text{}\mathrm{\Omega}$ at ${20}^{\circ}C$. At what temperature is its resistance equal to $33\text{}\mathrm{\Omega}$?

hottchevymanzm

Beginner2022-07-21Added 15 answers

Write the given values with suitable variables.

$a=2\times {10}^{-3}{/}^{\circ}C\phantom{\rule{0ex}{0ex}}{R}_{0}=30\text{}\mathrm{\Omega}\phantom{\rule{0ex}{0ex}}{T}_{0}=20{\text{}}^{\circ}C\phantom{\rule{0ex}{0ex}}R=33\text{}\mathrm{\Omega}$

Here, $\alpha ,{R}_{0},{T}_{0}$, and R are the coefficient of resistivity, initial resistance, initial temperature, and final resistance.

The final resistance of the material can be expressed as

$R={R}_{0}(1+\alpha (T-{T}_{0}))\phantom{\rule{0ex}{0ex}}(33\mathrm{\Omega})=(30\mathrm{\Omega})(1+(2\times {10}^{-3}{/}^{\circ}C)(T-{20}^{\circ}C))\phantom{\rule{0ex}{0ex}}T={70}^{\circ}C$

$a=2\times {10}^{-3}{/}^{\circ}C\phantom{\rule{0ex}{0ex}}{R}_{0}=30\text{}\mathrm{\Omega}\phantom{\rule{0ex}{0ex}}{T}_{0}=20{\text{}}^{\circ}C\phantom{\rule{0ex}{0ex}}R=33\text{}\mathrm{\Omega}$

Here, $\alpha ,{R}_{0},{T}_{0}$, and R are the coefficient of resistivity, initial resistance, initial temperature, and final resistance.

The final resistance of the material can be expressed as

$R={R}_{0}(1+\alpha (T-{T}_{0}))\phantom{\rule{0ex}{0ex}}(33\mathrm{\Omega})=(30\mathrm{\Omega})(1+(2\times {10}^{-3}{/}^{\circ}C)(T-{20}^{\circ}C))\phantom{\rule{0ex}{0ex}}T={70}^{\circ}C$

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