A piece of wire having equal resistance R is cut into 4 equal parts
1) compare resistance of each part with resistance of original wire
2) if 4 parts are connected in parallel, compare equivalent resistance with resistance of original wire.

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Solution

(a) We know that total resistance = R
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.

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A piece of wire having equal resistance R is cut into 4 equal parts 1) compare resistance of each part with resistance of original wire 2) if 4 parts are connected in parallel, compare equivalent resistance with resistance of original wire.

A piece of wire having equal resistance R is cut into 4 equal parts
1) compare resistance of each part with resistance of original wire
2) if 4 parts are connected in parallel, compare equivalent resistance with resistance of original wire.