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Chapter 14: Problem 49

The current at which a fuse wire melts does not depend on its (A) Cross-sectional area (B) Length (C) Resistivity (D) Density

Short Answer

Expert verified
The current at which a fuse wire melts depends on factors such as its cross-sectional area, length, and resistivity, but not directly on its density. Hence, the correct answer is (D) Density.

Step by step solution

01

Understanding Fuse Wire Properties

A fuse wire is a safety device used in electrical circuits to protect them from overloading and short circuits. It is designed to melt and break the circuit when the current flowing through it exceeds a specific value. The melting of the fuse wire depends on its ability to dissipate heat generated due to the flow of current, which in turn depends on the properties of the material used in the fuse wire.
02

Analyzing Cross-sectional Area

The cross-sectional area of the fuse wire determines how much current can flow through it before it melts. A larger cross-sectional area will allow more current to flow without heating up excessively, while a smaller cross-sectional area will heat up and melt faster. Therefore, the melting current of the fuse wire depends on its cross-sectional area.
03

Analyzing Length

The length of the fuse wire affects its overall resistance. A longer wire will have more resistance, and thus, generate more heat for a given current. The heat produced in the wire is directly proportional to the square of the current flowing through it and the resistance of the wire. Since a longer wire has a higher resistance, it will generate more heat and thus, might cause the fuse wire to melt at a lower current level. Therefore, the melting current of the fuse wire depends on its length.
04

Analyzing Resistivity

Resistivity is a property of the material which determines its resistance to current flow. A material with high resistivity generates more heat for a given current, which in turn, can cause the fuse wire to melt. The heat generated is proportional to the product of the resistivity and the square of the current flowing through the wire. Thus, the melting current of the fuse wire depends on its resistivity.
05

Analyzing Density

The density of a material is the mass per unit volume. It does not directly affect the resistance or heat generation in the fuse wire. The main factors affecting the melting current are the resistance and the heat dissipation capacity of the material. Density may indirectly affect these properties, but it is not a primary factor in determining the melting current of the fuse wire.
06

Conclusion

From the analysis of each factor, it is clear that the current at which a fuse wire melts does not directly depend on its density. Therefore, the correct answer is (D) Density.

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