Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

An electronic device designed to operate at any temperature in the range from \(-10.0°{\rm{C}}\) to \(55.0°\;{\rm{C}}\) contains pure carbon resistors. By what factor does their resistance increase over this range?

The resistance is increased by the factor \(1.03\).

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Concepts and Principles

The resistance of a conductor can be given in terms of the temperature as:

\(R = {R_0}\left( {1 + \alpha \left( {T - {T_0}} \right)} \right)\)

The value of \({R_0}\) is the resistance at some reference temperature, and the value of \({T_0}\) and the value of \(\alpha \) is the temperature coefficient of resistivity.

Step 2: The given data

The temperature coefficient of resistivity for carbo is: \(\alpha = - 0.5{\rm{ }} \times {\rm{ }}{10^{ - 3}}^ \circ \;{{\rm{C}}^{ - 1}}\)
Temperature range for which electronic device can be used from \( - {10.0^o}\;{\rm{C}}\) to \({55.0^o}\;{\rm{C}}\).

Step 3: Resistance of carbon in its upper and lower limit of temperature

Resistance of the carbon resistors corresponding to the lower limit of the temperature range is found from the above equation as:

\({R_{lower}} = {R_0}\left( {1 + \alpha \left( {{T_{lower}} - {T_0}} \right)} \right)\) ………………(I)

The value we take here is: \({T_0}{\rm{ }} = {\rm{ }}{20^\circ }\;{\rm{C}}\) which has to be the reference temperature.

Resistance of the carbon resistors corresponding to the upper limit of the temperature range is found from the above equation as:

\({R_{Upper}} = {R_0}\left( {1 + \alpha \left( {{T_{Upper}} - {T_0}} \right)} \right)\) …………….(II)

Step 4: Calculation of the carbon resistance, which increases over the temperature

Dividing the first equation with the second equation, we get:

\(\begin{align}\frac{{{R_{lower}}}}{{{R_{upper}}}}{\rm{ }} &= {\rm{ }}\frac{{{R_0}\left( {1 + \alpha \left( {{T_{lower}} - {T_0}} \right)} \right)}}{{{R_0}\left( {1 + \alpha \left( {{T_{Upper}} - {T_0}} \right)} \right)}}\\ &= {\rm{ }}\frac{{1 + \alpha \left( {{T_{lower}} - {T_0}} \right)}}{{1 + \alpha \left( {{T_{Upper}} - {T_0}} \right)}}\end{align}\)

Entering the values and we obtain is:

\(\begin{align}\frac{{{R_{lower}}}}{{{R_{upper}}}}{\rm{ }} &= {\rm{ }}\frac{{1 + ( - 0.5 \times {{10}^{ - 3}}^ \circ \;{{\rm{C}}^{ - 1}})( - {{10.0}^ \circ }\;{\rm{C}} - {{20.0}^ \circ }\;{\rm{C}})}}{{1 + ( - 0.5 \times {{10}^{ - 3}}^ \circ \;{{\rm{C}}^{ - 1}})({{55.0}^ \circ }\;{\rm{C}} - {{20.0}^ \circ }\;{\rm{C}})}}\\ &= \frac{{1.015}}{{0.9835}}\\ &= {\rm{ }}1.03\end{align}\)

Therefore, the factor by which the resistance increases is: \(1.03\).

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College Physics (Urone)

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Short Answer

An electronic device designed to operate at any temperature in the range from \(-10.0°{\rm{C}}\) to \(55.0°\;{\rm{C}}\) contains pure carbon resistors. By what factor does their resistance increase over this range?

Step by Step Solution

Step 1: Concepts and Principles

Step 2: The given data

Step 3: Resistance of carbon in its upper and lower limit of temperature

Step 4: Calculation of the carbon resistance, which increases over the temperature

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College Physics (Urone)

Answers without the blur.

Short Answer

An electronic device designed to operate at any temperature in the range from \(-10.0°{\rm{C}}\) to \(55.0°\;{\rm{C}}\) contains pure carbon resistors. By what factor does their resistance increase over this range?

Step by Step Solution

Step 1: Concepts and Principles

Step 2: The given data

Step 3: Resistance of carbon in its upper and lower limit of temperature

Step 4: Calculation of the carbon resistance, which increases over the temperature

Most popular questions for Physics Textbooks

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