Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Of what material is a resistor made if its resistance is \({\bf{40}}{\bf{.0}}\;{\bf{\% }}\)greater at than at \({\bf{20}}{\bf{.0°}}\;{\bf{C}}\)?

The wire is made from the material known as Iron.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Define Resistance

In an electrical circuit, the flow of current varies with the variation in resistance

In an electrical circuit, the flow of current varies with the variation in resistance.

The resistance of a conductor can be given 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 3: The given data

The initial temperature of the wire is: \({T_0} = 20^\circ \;{\rm{C}}\).

The resistance of the wire is forty percent greater at \(T = {100^\circ }\;{\rm{C}}\) than at \({T_0}\).

Step 4: Evaluating the material

The resistance of the wire is expressed as a function of temperature change by the equation as:

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

As the resistance of the wire is forty percent at temperature \(T\) than at temperature\({T_0}\), the resistance of the wire will be:

\(\begin{align}R{\rm{ }} &= {\rm{ }}{R_0} + 40\;\% \left( {{R_0}{\rm{ }}} \right)\\ &= {\rm{ }}1.40{R_0}\end{align}\)

Substitute the values in equation 1, and we get:

\(\begin{align}1.40{R_0}{\rm{ }} &= {\rm{ }}{R_0}\left( {1 + \alpha \left( {T - {T_0}} \right)} \right)\\1.40{\rm{ }} &= {\rm{ }}1 + \alpha \left( {T - {T_0}} \right)\end{align}\)

Rearranging and solving for \(\alpha \):

\(\begin{align}1.40 - 1{\rm{ }} &= {\rm{ }}\alpha \left( {T - {T_0}} \right)\\0.40{\rm{ }} &= {\rm{ }}\alpha \left( {T - {T_0}} \right)\\\alpha {\rm{ }} &= {\rm{ }}\frac{{0.40}}{{T - {T_0}}}\end{align}\)

Entering the values for \(T\) and \({T_0}\), we obtain:

\(\begin{align}\alpha {\rm{ }} &= {\rm{ }}\frac{{0.40}}{{{{100}^\circ }\;{\rm{C }} - {{20}^\circ }\;{\rm{C}}}}\\ &= {\rm{ }}5.00 \times {10^{ - 3}}^\circ \;{{\rm{C}}^{ - 1}}\end{align}\)

We do observe that this coefficient of resistivity is related to iron.

Therefore, the wire is made of Iron.

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College Physics (Urone)

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Short Answer

Of what material is a resistor made if its resistance is \({\bf{40}}{\bf{.0}}\;{\bf{\% }}\)greater at than at \({\bf{20}}{\bf{.0°}}\;{\bf{C}}\)?

Step by Step Solution

Step 1: Define Resistance

In an electrical circuit, the flow of current varies with the variation in resistance.

Step 3: The given data

Step 4: Evaluating the material

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College Physics (Urone)

Answers without the blur.

Short Answer

Of what material is a resistor made if its resistance is \({\bf{40}}{\bf{.0}}\;{\bf{\% }}\)greater at than at \({\bf{20}}{\bf{.0°}}\;{\bf{C}}\)?

Step by Step Solution

Step 1: Define Resistance

In an electrical circuit, the flow of current varies with the variation in resistance.

Step 3: The given data

Step 4: Evaluating the material

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