Question
Sat April 30, 2011 By: Bhavya Garg

Q. A wire of resistance 4R is bent in the form of a circle . What is the effective resistance between the ends of the diameter?

Expert Reply
Sat April 30, 2011
Let 'l' be the length of the wire and 'a' the area of cross-section;
then 4R = ?l/a
or, l/a = 4R/ ?
Between the ends of the diameter, length of the circle = ?r = l/2
or, l = 2?r
Therefore, the effective resistance between the ends of the diameter,
R' = ?(?r)/a = ? (l/2) /a =?l/2a
or, R' = (?/2)(l/a) = (?/2)(4R/?) = 2 R
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