Finding diameter of a wire based on the current and current density.

In summary, the conversation is about designing a fuse with a current rating of 0.9 A and a material that melts at a current density of 540 A/cm2. The fuse needs to "blow" if the current exceeds 0.9 A. To determine the diameter of wire needed, the formula J=I/A was used, where J is the current density, I is the current, and A is the area. However, the final answer in millimeters may be incorrect due to unit inconsistencies.
  • #1
mkienbau
12
0
You need to design a 0.9 A fuse that "blows" if the current exceeds 0.9 A. The fuse material in your stockroom melts at a current density of 540 A/cm2. What diameter wire of this material will do the job?

540x10^-2=5.40 A/m^2

5.40= .9/x

Solving for x gives the answer: .166666666666667

Then:

.166666666667=pi(r^2)

sqrt(.166666666667/pi)=r

The result of that answer multiplied by 2 gives 4.607m. The answer asks for it in mm so I converted to 460.7mm and it says its wrong. Where did I go wrong, I'm just using the current density formula: J=I/A

Where J is the current density
I is the current
A is the area
 
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  • #2
mkienbau said:
You need to design a 0.9 A fuse that "blows" if the current exceeds 0.9 A. The fuse material in your stockroom melts at a current density of 540 A/cm2. What diameter wire of this material will do the job?

540x10^-2=5.40 A/m^2

5.40= .9/x

Solving for x gives the answer: .166666666666667

Then:

.166666666667=pi(r^2)

sqrt(.166666666667/pi)=r

The result of that answer multiplied by 2 gives 4.607m. The answer asks for it in mm so I converted to 460.7mm and it says its wrong. Where did I go wrong, I'm just using the current density formula: J=I/A

Where J is the current density
I is the current
A is the area
Do what you did again, only this time keep track of your units every step along the way. Unit consistency will do wonders for you.
 
  • #3


Your calculations and approach are correct. The issue may lie in the conversion from meters to millimeters. You may have made a mistake in the conversion, or the answer may require a more precise value. I would recommend double-checking your calculations and using a calculator with a higher precision to get a more accurate answer. Additionally, you may want to check if the answer requires a specific number of significant figures.
 

1. What is the formula for finding the diameter of a wire based on current and current density?

The formula for finding the diameter of a wire based on current and current density is: d = 2 * (I / J)^0.5, where d is the diameter, I is the current, and J is the current density.

2. How do I measure the current and current density of a wire?

The current can be measured using an ammeter, while the current density can be calculated by dividing the current by the cross-sectional area of the wire.

3. Can the diameter of a wire change if the current or current density changes?

Yes, the diameter of a wire can change if the current or current density changes. As the current or current density increases, the diameter of the wire will decrease and vice versa.

4. How accurate is the formula for finding the diameter of a wire?

The formula for finding the diameter of a wire based on current and current density is accurate for ideal conditions. Factors such as temperature, material properties, and external influences can affect the accuracy of the formula.

5. Are there any potential applications for knowing the diameter of a wire based on current and current density?

Knowing the diameter of a wire based on current and current density can be useful in various industries, such as electrical engineering, telecommunications, and automotive. It can also help in accurately predicting the behavior and performance of wires in different systems.

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