Question

A metal wire of resistance R is cut into eight equal pieces that are then placed together side by side to form a new cable with a length equal to one-eight the original length. What is the resistance of this new cable

Answer 1

R / 64

Step-by-step explanation:

Let he length of the wire is L and its resistance is R.

The resistance of the wire is directly proportional to the length of the wire. As the wire is cut into 8 equal pieces so the resistance of small wire is R/8.

Now they are connected in parallel.

The equivalent resistance is given by

`(1)/(R_(eq))= 8* (8)/(R)`

`R_(eq)=(R)/(64)`

Thus, the equivalent resistance of the new cable is R / 64.