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

Answer:

R / 64

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

$\frac{1}{R_{eq}}= 8\times \frac{8}{R}$

$R_{eq}=\frac{R}{64}$

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