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a wire of resistance 12 ohms is bent in the form of circle.what is the effective resistance between a and b?

OCW Scholar - Physics II: Electricity and Magnetism
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|dw:1357465781135:dw|
12 ohms
0

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Other answers:

Can you please tell me, how to solve this problem?
3 ohms
@pdvpa please explain
Yes, I think 3 ohms is right. Each semi-circle between A and B is 6 ohms (half the 12 ohms of the full wire). Two 6 ohm wires in parallel is equivalent to one 3 ohm wire. No need to use the formula, the area across each wire is added when they are side by side so the resistance is halved to 3 ohms.
how could you consider it as two sepearte pieces when they are a single entity of a wire made of a material having 12 ohm resistance..
3 ohms
Hi mathavraj, Yes you are right, the wire is a single piece that forms a circle. Your drawing shows A opposite B. There are two paths for the electricity or current to flow from A to B. As each path appears to be the same length (A opposite B on the circle) each path will have a resistance of 6 ohms because it is half the length of the full wire. Two 6 ohms paths in parallel (sharing the current flow) is equivalent to one 3 ohm path between A and B.
im sorry @oceanok i still dont get it..
|dw:1362654142306:dw| Hi, Good morning mathavraj, hope you are well. We are clearly thinking about the problem in different ways. I will try to understand how you are thinking. The current does not flow in a circle around the full length of the wire. Forget for the moment that the circle was made from a single length of wire and just approach the problem as it is now. Imagine a stream with water flowing down from a high point at A to a low point at B. The stream divides in two. Each side is a semi-circle (the shape is not that important) both of equal length. The sides meet again at B to form a single stream again. It is the same with the electrical circuit. The current enters at A divides into two equal amounts (both flowing towards B). The flow of current is eased because each semi -circle is only half the length of the original wire, so each side is 6 ohms. Also each side is now sharing the overall flow from A to B so the total resistance is halved again to 3 ohms. This circle froms part of the circuit with perhaps a battery connected between A and B. The current is not flowing in a circle around the 12 ohm wire but flowing from A to B in two sides of the circle. The original wire is joined at the open ends to form a circle, it is not open ended.
@oceanoak thanks man..nw i get it...:)

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