Concept explainers
A
The resistance of the tapered wire.
Answer to Problem 82PQ
The resistance of the tapered wire is
Explanation of Solution
The diagram of the tapered wire is given in Figure P28.82. The length of the wire is
From the geometry of the longitudinal section of the wire, it can be deduced that,
Here,
From equation (I), write the expression for the radius at a distance
Write the general expression for the resistance of the wire.
Here,
Since the cross-sectional area of the wire changes as the distance
Use equation (II) in (IV).
Integrate equation (V) with the limits
Take
Use
Reduce equation (VIII).
Conclusion:
Therefore, the resistance of the tapered wire is
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Chapter 28 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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