Resistance Physics Problem?

Question

A length of wire is cut into five equal pieces. The five pieces are then connected in parallel, with the resulting resistance being 61.0 ohms. What was the resistance of the original length of wire before it was cut up?

The answer I first arrived at was 305 but I am positive that this is not the right answer.

Answer 1

You were on the right track with your answer of 305 ohms, but you forgot the last step to multiply by 5 again to get the total resistance of the entire length of wire, not just 1/5 of the total length.

Recalling the equation used to calculate parallel resistance, we know that
(61.0 ohms)^-1 = (x)^-1 + (x)^-1 + (x)^-1 + (x)^-1 + (x)^-1,
Which equals,
(61.0 ohms)^-1 = 5 * (x)^-1,
Where x is the resistance of a single segment of the wire equal to 1/5 of the total length.
We can solve for x as,
x = ((61 ohms)^-1 / 5 segments)^-1
x = 305 ohms per segment

But this is just 1/5 of the total wire. If the wire were all in one piece, it would be like having 5 of these resistors in series, in which case the resistance adds and would be equal to 5 times the value of just one segment.
R_total = x + x + x + x + x = 5 * x

Total resistance of the original length of wire = 1525 Ohms.

Answer 2

Don't memorize the formula for parallel resistance. Work from first priciples.

Let Rp = 61, the || resistance. Let Rs be the resistance a section

current is conserved, and voltage drop is the same:
Vp = Vs
I*Rp = (I/5)*Rs

Rs = 5*Rp = 5*61 = 305

but, this is the resistance for one piece. The original piece is a series of 5 of these
so,
Ro = 5*R = 1525 ohms.

Answer 3

305 Ohms is the right answer.
5 * 61 = 305
There might be some artifacts from the connections or the wire might not be perfectly linear.
There cannot be any artifacts from inductive reactance, since you said "resistance" and not impedence.
Oops. I am wrong. The next guy is right. Multiply by 5 again.
= 1525 Ohms.

Answer 4

61 * 5 * 5 = 1525 ohms

This is a psychology problem. Five and then five... the second five seems redundant and is likely filtered out by the brain to prevent overloading.