Minimum Wire Length Calculation for Square Pattern in 10cm Square

In summary, the problem asks for the minimum value of ##x## that minimizes the total length ##l##, which is the length of the horizontal segment in the middle of the square. The given method involves extending the segment to create a triangle and using Pythagoras' theorem to find the length of the wire. Then, differentiating with respect to ##x## and solving for the minimum value of ##x## will give the minimum length of the wire. However, there may be an issue with the problem statement as it does not specify any constraints on the possible values of ##x##.
  • #1
squenshl
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Homework Statement


A wire pattern is inserted into a ##10##cm square by making a horizontal line in the middle of the square (not all the way across and with length ##x##) and connecting the ends of this line to the closest two corners. What is the minimum value of ##x##?

Homework Equations

The Attempt at a Solution


Let ##y## be the length of the wire from the end of ##x## to the corner of the square. This means the total length of the wire is ##l = x+4y##.

I extended the blue line ##x## to create a triangle then I used Pythagoras' to get ##y^2 = 25+\frac{(10-x)^2}{4}##.

Do I then throw this (meaning ##y##) into ##l## then differentiate with respect to ##x## then solve to get my minimum value for ##x## then ##y## which would give me the minimum length for ##l##.

Thanks!
 

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  • #2
squenshl said:

Homework Statement


A wire pattern is inserted into a ##10##cm square by making a horizontal line in the middle of the square (not all the way across and with length ##x##) and connecting the ends of this line to the closest two corners. What is the minimum value of ##x##?

Homework Equations

The Attempt at a Solution


Let ##y## be the length of the wire from the end of ##x## to the corner of the square. This means the total length of the wire is ##l = x+4y##.

I extended the blue line ##x## to create a triangle then I used Pythagoras' to get ##y^2 = 25+\frac{(10-x)^2}{4}##.

Do I then throw this (meaning ##y##) into ##l## then differentiate with respect to ##x## then solve to get my minimum value for ##x## then ##y## which would give me the minimum length for ##l##.

Thanks!

If that is what you think you should do, why ask us? Just do it!

The point is that you need to start having confidence in your own methods, and you need to be willing to make a mistake, perhaps spending a lot of time on an erroneous approach, then throwing out the worksheets and starting again. That is how all of the homework helpers learned the subject!
 
  • #3
The problem statements seems to be ill at least to me. The problem asks for the minimum value of ##x ##(which if understand correctly is the length of the segment in the middle of square). What prevents us from taking ##x=0##?
The only thing I can make is that you probably meant to say the value of ##x## that minimizes the total length ##l## cause that's what your method calculates.
 
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  • #4
Delta2 said:
The problem statements seems to be ill at least to me. The problem asks for the minimum value of ##x ##(which if understand correctly is the length of the segment in the middle of square). What prevents us from taking ##x=0##?
The only thing I can make is that you probably meant to say the value of ##x## that minimizes the total length ##l## cause that's what your method calculates.
what he said (very small).jpg
 

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Related to Minimum Wire Length Calculation for Square Pattern in 10cm Square

1. What is the minimum length of wire required for a circuit?

The minimum length of wire required for a circuit depends on the specific application and the amount of current flowing through the wire. In general, the longer the wire, the higher the resistance and the lower the current that can flow through it. Therefore, the minimum length of wire needed for a circuit will vary based on the desired current and the resistance of the wire.

2. How do I calculate the minimum length of wire for a circuit?

To calculate the minimum length of wire for a circuit, you will need to know the resistance of the wire and the desired current. Using Ohm's Law (V=IR), you can solve for the length of wire needed by dividing the desired current by the resistance.

3. What happens if I use a wire that is shorter than the minimum length?

Using a wire that is shorter than the minimum length needed for a circuit can result in a higher resistance and a lower current flow. This can lead to decreased efficiency and potential overheating of the wire, which can be dangerous. It is important to use the appropriate length of wire for a circuit to ensure safe and efficient operation.

4. Is there a minimum length of wire required for all circuits?

No, the minimum length of wire needed for a circuit will vary depending on the specific application and the components being used. Some circuits may require longer wire lengths to accommodate for larger currents or to reduce resistance, while others may require shorter lengths for more precise control.

5. How can I ensure I am using the correct minimum length of wire for my circuit?

To ensure you are using the correct minimum length of wire for your circuit, it is important to calculate the length using the appropriate formula (V=IR) and to consider the specific needs of your circuit. Additionally, consulting with a qualified electrician or engineer can help ensure that you are using the correct wire length for your specific application.

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