A uniform wire of resistance is cut into five equal parts. These parts are now connected in parallel. Calculate the equivalent resistance of the combination.
Step 1: Given information
Wire cuts in five equal parts.
Step 2: To find
We have to find the equivalent resistance of the combination.
Step 3: Calculate each resistance of the combination
We know the relation,
is the length of the conductor and is the resistance of the conductor.
Whenever the wire is split into five equal sections, the length of each portion decreases by one-fifth, as does the resistance of each part.
Step 3: Calculate the equivalent resistance of the combination
Use the expression for equivalent resistors in parallel,
Therefore, the equivalent resistance is .