A wire of resistance R is bent into a circle. Find the resistance across the diameter.
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if the resistance of wire is given as R
bent in to circle
across the diameter the upper part of wire and bottom part of wire equally dived and resistance becomes R/2 each
now when we calculate the resistance across diameter the upper part and bottom part are parallel to each other
therefore 1/Req = 1/R1 + 1/R2
1/Req = 1/(R/2) + 1/(R/2)
= 2/R + 2/R
= 4/R
therefore Req = R/4
bent in to circle
across the diameter the upper part of wire and bottom part of wire equally dived and resistance becomes R/2 each
now when we calculate the resistance across diameter the upper part and bottom part are parallel to each other
therefore 1/Req = 1/R1 + 1/R2
1/Req = 1/(R/2) + 1/(R/2)
= 2/R + 2/R
= 4/R
therefore Req = R/4
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