Question

A piece of wire having resistance R is cut into four equal parts.
a)How does the resistance of each part compare with the original resistance

Answer 1

(1)

(a)

the resistance is given as

R = ρl/A

where

ρ = resistivity

l = length of the resistor

A = area of cross-section

now, if the resistor is cut into four equal parts, let the length of each part will be l' = l/4

so, the each new resistance will be

R' = ρl'/A = ρl / 4A = (1/4).(ρl/A) = R/4

thus, the resistance of each resistor will reduce to quarter its original value.