Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Calculate $d ρ / d T$ at room temperature for (a) copper and (b) silicon, using data from Table 41-1.

The value of $d ρ / d T$ at room temperature for copper is $8 \times 10^{- 11} Ω . m / K$ .
The value of $d ρ / d T$ at room temperature for silicon is $- 2.1 \times 10^{2} Ω . m / K$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

From the value of Table 41-1:

Resistivity of copper, $ρ_{C u} = 2 \times 10^{- 8} Ω . m$
Temperature coefficient of resistivity of copper, $α_{C u} = 4 \times 10^{- 3} K^{- 1}$
Resistivity of silicon, $ρ_{S i} = 3 \times 10^{3} Ω . m$
Temperature coefficient of resistivity of silicon, $α_{S i} = - 70 \times 10^{- 3} K^{- 1}$

Step 2: Understanding the concept of rate of resistivity

The rate of change of resistivity is positive for conductors whereas for semiconductors it is negative. Thus, the resistance of conductors increase with increase in temperature and the resistance of semiconductors decrease with increase in temperature.

Formula:

The rate of resistivity of a material, $d ρ / d T = ρ α$ (i)

Step 3: a) Calculation for the rate of resistivity of copper

Using the given data in equation (i), we can get the value of for the copper material as follows:

${(d ρ / d T)}_{C u} = (2 \times 10^{- 8} Ω . m) (4 \times 10^{- 3} K^{- 1}) = 8 \times 10^{- 11} Ω . m / K$

Hence, the value of is $8 \times 10^{- 11} Ω . m / K$ .

Step 4: b) Calculation for the rate of resistivity of silicon

Using the given data in equation (i), we can get the value of for the copper material as follows:

${(d ρ / d T)}_{S i} = (3 \times 10^{3} Ω . m) (- 70 \times 10^{- 3} K^{- 1}) = - 2.1 \times 10^{2} Ω . m / K$

Hence, the value of is $- 2.1 \times 10^{2} Ω . m / K$ .

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Fundamentals Of Physics

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Short Answer

Calculate $d ρ / d T$ at room temperature for (a) copper and (b) silicon, using data from Table 41-1.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of rate of resistivity

Step 3: a) Calculation for the rate of resistivity of copper

Step 4: b) Calculation for the rate of resistivity of silicon

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Fundamentals Of Physics

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Short Answer

Calculate dρ/dT at room temperature for (a) copper and (b) silicon, using data from Table 41-1.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of rate of resistivity

Step 3: a) Calculation for the rate of resistivity of copper

Step 4: b) Calculation for the rate of resistivity of silicon

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Calculate $d ρ / d T$ at room temperature for (a) copper and (b) silicon, using data from Table 41-1.