Dividing Resistance Wire: How Many Parts?

[Noiro]

Homework Statement

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?

Homework Equations

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

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 equation should be

R.tot=R/n

otherwise it's fine

 

[Noiro]

Thank you very much, Ofey!