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Electricity and Magnetism
Level
2
A wire has resistance 12 ohms. It is bent in the form of a circle. What is the effective resistance between the two points on any diameter of the circle?
The answer is 3.
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1 solution
After bending wire total resistance is still R. Along any diameter the circle is divided into 2 segments ie resistance of each segment is halved ie R/2. these 2 segments are connected in parallel => 1/R = (1/R/2 ) + (1/R/2) = 2/R + 2/R = 4/R => R = R/4 = 12/4 = 3 ohms.