(a)
The relationship between the diameter and the length of the wire.
(a)
Answer to Problem 28P
The relationship between the diameter and the length of the wire is
Explanation of Solution
Write the expression for the output power of the heater.
Here,
Write the expression for the
Here,
Use equation (II) in (I) to solve for
Write the expression for power relating the resistance.
Here,
Use equation (IV) to solve for
Write the expression for the resistivity.
Here,
Write the expression for resistance.
Here,
Write the expression for
Here,
Use equation (VIII) in (VII) to solve for
Use the unit conversion
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the relationship between the diameter and the length of the wire is
(b)
The volume of the nichrome wire is less than
(b)
Answer to Problem 28P
Explanation of Solution
Write the expression for the volume.
Here,
Use equation (VIII) in (X) to solve for
Use the relation obtained from part (a),
Use equation (XII) in (XI) to solve for
Use equation (XIII) in (XII) to solve for
Conclusion:
Substitute
Substitute
Therefore, the volume
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Chapter 21 Solutions
Principles of Physics: A Calculus-Based Text
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