Dividing Resistance Wire: How Many Parts?

In summary, the problem involves a 100 ohm resistance wire being cut into equal parts and combined in parallel, resulting in a total resistance of 1 ohm. Using the equations R=nR and R.tot=R/n, we can determine that the wire was cut into 10 equal parts.
  • #1
Noiro
24
0

Homework Statement



100[tex]\Omega[/tex] resistance wire is cut in equal parts, which are combined in parallel. They're total resistance is 1[tex]\Omega[/tex]. In how many parts the wire is cut?

Homework Equations



I guess it's something like [tex]R[/tex]=[tex]\frac{R_{1}}{N}[/tex]

The Attempt at a Solution


I don't have an idea how to solve it :frown: I would be very grateful if someone could help me solve this problem.
 
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  • #2
Think of the resistance wire as many small resistors connected together. Because the resistors are connected together in a series, the total resistanse in the "first" situation will be

nR=100 (1)

Here "n" is the number of resistors (number of resistanse wire parts) and R is the resistanse of a part of resistanse wire. Since the pieces are cut in identical pieces they will also have the same "independent" resistanse.

Further we know that if we combine the parts in parallel we get the resistanse as

1/(R.tot)=1/(R.1)+1/(R.2)+1/(R.3)...

Because R.1=R.2=R.3... (and so forth) we get

1/(R.tot)=n/(R.1)

Or

R.tot=R=n (2)

Again, R.1=R.2=R.3 because the pieces are identical

Solving for (1) and (2) gives that we have 10 pieces.
 
  • #3
Sorry for my hasty reply, the second equation should be

R.tot=R/n

otherwise it's fine
 
  • #4
Thank you very much, Ofey!
 

Related to Dividing Resistance Wire: How Many Parts?

1. What is electricity?

Electricity is the flow of tiny particles called electrons through a material, such as a wire. These electrons carry energy and can power various devices and machines.

2. How is electricity generated?

Electricity can be generated in various ways, such as through burning fossil fuels, harnessing the power of falling water, or using renewable sources like solar or wind energy. The most common method is through generators, which convert mechanical energy into electrical energy.

3. What is the difference between AC and DC electricity?

AC (alternating current) and DC (direct current) are two types of electrical currents. AC electricity is constantly changing direction, while DC electricity flows in one direction. AC is typically used for powering homes and businesses, while DC is commonly used in batteries and electronic devices.

4. How is electricity distributed?

Once electricity is generated, it travels through a complex system of power lines, transformers, and substations to reach homes and businesses. The distribution grid is designed to carry electricity safely and efficiently to different areas.

5. What are the safety precautions when dealing with electricity?

Electricity can be dangerous, so it is important to take proper precautions when dealing with it. Always turn off the power source before working with electrical wiring, wear protective gear, and never touch exposed wires or outlets. It is also important to have a qualified electrician handle any complex electrical work.

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