Resistance and Wire Length

Part A = R_{Long} / n^{2}

**Solution Below:**

You have been given a long length of wire. You measure the resistance of the wire, and find it to be R

_{long}. You then cut the wire into n identical pieces (Intro 1 figure) .

Part A

If you connect the n pieces in parallel as shown (Part A figure), what is the total resistance R

Express your answer in terms of R

_{total}of the n wires connected in parallel?Express your answer in terms of R

_{long}and n.Each individual piece has a resistance of r = R_{Long} / n (since the sizes are all the same).

Since the new resistors are in parallel, the overall resistance is given by R_{total} = (n * (1/r))^-1

So:

R_{total} = (n * (1/r))^-1

R_{total} = (n * (1/(R_{Long}/n))^-1

R_{total} = (n * (n/R_{Long}))^-1

R_{total} = (n^{2}/R_{Long})^-1

R_{total} = R_{Long} / n^{2}

R_{Long} / n^{2}