## mathavraj 2 years ago a wire of resistance 12 ohms is bent in the form of circle.what is the effective resistance between a and b?

1. mathavraj

|dw:1357465781135:dw|

2. sttevegoodnatured

12 ohms

3. sttevegoodnatured

0

4. Kathi26

Can you please tell me, how to solve this problem?

5. mathavraj

@ghazi @evergirl @mathslover help..

6. pdvpa

3 ohms

7. mathavraj

8. mathavraj

@ujjwal

9. oceanoak

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.

10. mathavraj

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..

11. saitejab

3 ohms

12. oceanoak

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.

13. mathavraj

im sorry @oceanok i still dont get it..

14. oceanoak

|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.

15. mathavraj

@oceanoak thanks man..nw i get it...:)