Mastering Physics Solutions: Resistance and Wire Length

Resistance and Wire Length

Part A = RLong / n2

Solution Below:

You have been given a long length of wire. You measure the resistance of the wire, and find it to be Rlong. You then cut the wire into n identical pieces (Intro 1 figure) .

Mastering Physics Solutions: Resistance and Wire Length

Part A

If you connect the n pieces in parallel as shown (Part A figure), what is the total resistance Rtotal of the n wires connected in parallel?
Express your answer in terms of Rlong and n.

Mastering Physics Solutions: Print ViewResistance and Wire Length

Each individual piece has a resistance of r = RLong / n (since the sizes are all the same).
Since the new resistors are in parallel, the overall resistance is given by Rtotal = (n * (1/r))^-1

So:

Rtotal = (n * (1/r))^-1
Rtotal = (n * (1/(RLong/n))^-1
Rtotal = (n * (n/RLong))^-1
Rtotal = (n2/RLong)^-1
Rtotal = RLong / n2

RLong / n2

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