Question

A piece of wire having resistance r is cut into four equal parts how does the resistance of each part compared with the original resistance be a four parts of join together in parallel how will resistance of combination will the with the resistance of original wire

Answer 1

Original resistance = r ohms

After cutting in 4 parts,

Resistance of each part = r/4 ohms

Net resistance when connected in parallel,

1/r' = 4/r + 4/r + 4/r + 4/r

1/r' = 16/r

r' = r/16 ohms

Therefore resistance becomes 1/16 times

Ratio = Resistance of combination: Original Resistance = r':r = r/16:r = 1:16