# Need help with electricity

#### Noiro

1. The problem statement, all variables and given/known data

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

2. Relevant equations

I guess it's something like $$R$$=$$\frac{R_{1}}{N}$$

3. The attempt at a solution
I don't have an idea how to solve it I would be very grateful if someone could help me solve this problem.

#### Ofey

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.

#### Ofey

Sorry for my hasty reply, the second eqation should be

R.tot=R/n

otherwise it's fine

#### Noiro

Thank you very much, Ofey!

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving