The equivalent resistance of n resistors connected in parallel is given by
(1)
In our problem, the resulting resistance of the 5 pieces connected in parallel is
, and since the 5 pieces are identical, their resistance R is identical, so we can rewrite (1) as
From which we find
.
So, each piece of wire has a resistance of
. Before the wire was cut, the five pieces were connected as they were in series. The equivalent resistance of a series of n resistors is given by
So if we apply it at our case, we have
therefore, the resistance of the original wire was
.
In our problem, the resulting resistance of the 5 pieces connected in parallel is
From which we find
So, each piece of wire has a resistance of
So if we apply it at our case, we have
therefore, the resistance of the original wire was