Question

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 piecesIf you connect the n  pieces in parallel as shown , what is the total resistance  R_total of the n wires connected in parallel? Express your answer in terms of R_long and n.

Answer 1

The resistance of long wire = R

The resistance of each wire with in 'n' pieces, r = R/n

These 'n' number of resistors are connected in parallel. Then the total resistance is

given by

       R' = 1 / {(1/r) + (1/r) + ---------- upto n numbers of resistors}

       R' = 1 / (n/R)

       R' = r / n, But we have r = R/n, then

       R' = ( R/n) / n

       R' = R/n^2

So the total resistance R of the n wires connected in parallel is given by R/n^2.