Question

A metal wire of resistance 48 ???? is cut into four equal pieces that are then connected side by side to make a new wire that is one-quarter of the original length. What is the resistance of this new wire?

Answer 1

Answer:

Explanation:

Resistance of wire, R = 48 ohm

It is cut into four pieces.

As we know that the resistance is directly proportional to the length of the wire.

So, the resistance of each piece of wire, R' = 48 / 4 = 12 ohm

Now the four pieces are connected in parallel. So the equivalent resistance is given by

$\frac{1}{R_{eq}}=\frac{1}{R'}+\frac{1}{R'}+\frac{1}{R'}+\frac{1}{R'}$

$\frac{1}{R_{eq}}=\frac{1}{12}+\frac{1}{12}+\frac{1}{12}+\frac{1}{12}$

Req = 3 ohm