(Solved) 5 pieces of wire are connected in parallel & resulting resistance 2 ohms, what was the resistance of the wire?

soccerkid12

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11 years ago

5 pieces of wire are connected in parallel & resulting resistance 2 ohms, what was the resistance of the wire?

Here's the full question:
A length of wire is cut into 5 equal pieces. The 5 pieces are then connected in parallel, with the resulting being 2.0 ohms. What was the resistance of the original length of wire before it was cut up?
What's the answer and how do you do it?

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fireman

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11 years ago

For parallel resistors:

R(eff) = 1/((1/R1) + (1/R2) + (1/R3) +.....)

so if there are 5 and the R values are all equal,

R(eff) = 1/(5/R) = 2 ohm
R/5 = 2
R = 10 ohms (for each piece)

So the total resistance of the original wire was 50 ohms

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nygiantsfan

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11 years ago

Before they were cut, the wires were effectively in series, so their resistances added. Let R be the resistance of the total length of wire, and let r be the resistance of each of the 5 sublengths. We know that R = r+r+r+r+r = 5r. let the parallel resistance of the wires be p. 1/p = 1/r + 1/r + 1/r + 1/r + 1/r = 5/r so r = 5p. R = 5r = 5(5p) = 25p, or R = 50 ohms.

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otorres

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11 years ago

Since the wire pieces are in parallel, letting the resistance of each wire piece = R

(for a parallel, sum of reciprocal of resistances = reciprocal of total resistance)

1/R + 1/R + 1/R + 1/R + 1/R = 1/2, because each piece is equal in length and from the same wire, so they should have identical resistance.

5/R = 1/2
5 = R/2
R = 10 ohms

So the resistance of each wire is 10 ohms.
The resistance of the wire is directly proportional to its length, so let's say that each 10 ohm wire piece has a length of 2m, making the original wire 10m, letting resistance of original wire = x:

10/2 = x/10
100 = 2x
x = 50 ohms

So the resistance of the original wire = 50 ohms.

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microbiology1

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11 years ago

This verified answer contains over 120 words.

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5 pieces of wire are connected in parallel & resulting resistance 2 ohms, what was the resistance of the wire?

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