Question

You have been given a long length of wire. You measure the resistance of the wire, and find it to be \(R_{\text {long. }}\) You then cut the wire into \(n\) identical pieces (Figure 1).

Part A If you connect the n pieces in parallel as shown (Figure 2) , what is the total resistance R total of the n wires connected in parallel?

Answer 1

let resistance of each piece be (r)
>>> series combination >> I (current) same through each piece
R (long) = r + r + .... r >>> (n terms) = n r
R (long) = n r -------- (1)
=============
when connected in parallel > let R(total) be equivalent resistance parallel combination
1/R(total) = (1/r) + (1/r) + .... (1/r) [n terms]
1/R(total) = (n/r) .............. use (1)
1/R(total) = (n) [n / R (long)]
flip
R(total) = R (long) /n^2
relation required