Question

A piece of wire having R is cute into 4equal parts.(a) how will the resistor of each part compare with the original resistance?(b) if the four parts are placed in parallel, how will you joint resistance compare with the resistance of the original wire?

Answer 1

Hi.

We know that total resistance = R

(a)So, when the wire is cut into four equal parts, we actually have divided the total resistance into 4 equal parts. Hence, the resistance of each part is now 1/4th of the original Resistance, i.e. R/4..

(b) When these 4 parts are joined in parallel, the equivalent resistance Rp will be

1/Rp = 4/R + 4/R + 4/R + 4/R = 4(4/R) = 16/R
i.e. Rp = R/16 So, the joint resistance = R/16, i.e., 1/16th times of R




Hope this helps u!