Effective Resistance if bent in the form a circle

In summary, a wire with a resistance of 8R formed into a circle has an effective resistance between the ends of diameter AB that is equivalent to having two resistors in parallel. This is because the current entering at A has two possible paths, both involving a resistance of 4R (half the circumference of the circle). The combined resistance can be found by adding 4R and 4R in parallel. The use of the reciprocal formula is to account for this parallel connection.
  • #1
logearav
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Homework Statement



A wire of resistance 8R is bent in the form of a circle. What is the effective resistance between the ends of a diameter AB?


Homework Equations


I have attached the image and my attempt to solve it as told by my teacher.


Homework Equations





The Attempt at a Solution


But I don't know why the reciprocal formula is used. Please help.

 

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  • #2
It's because it is equivalent to having two resistors in parallel.
The current entering at A has a choice of 2 directions.
Both involve taking a path that is 4R. That is, half the resistance of the complete wire. (Round half the circumference to B.)
So to find the combined resistance, you need to add 4R and 4R in parallel.
 
  • #3
Thanks a lot stonebridge. Your help is very much appreciated
 

1. What is "Effective Resistance if bent in the form a circle"?

Effective Resistance if bent in the form a circle is a concept in physics that refers to the overall resistance of a circular circuit. It takes into account the individual resistances of each component in the circuit as well as the layout and arrangement of the components.

2. How is "Effective Resistance if bent in the form a circle" calculated?

To calculate the effective resistance of a circular circuit, you must first determine the individual resistances of each component in the circuit. Then, you can use the formula R = (r1 * r2)/(r1 + r2) where r1 and r2 are the individual resistances. This formula can be applied for any number of components in the circular circuit.

3. What factors affect the "Effective Resistance if bent in the form a circle"?

The effective resistance of a circular circuit is affected by the individual resistances of each component, the arrangement of the components, and the overall layout of the circuit. The direction and magnitude of the current flowing through the circuit can also impact the effective resistance.

4. Can the "Effective Resistance if bent in the form a circle" be greater than the individual resistances?

Yes, it is possible for the effective resistance of a circular circuit to be greater than the individual resistances of each component. This can occur when the components are arranged in a way that increases the overall resistance of the circuit.

5. How does "Effective Resistance if bent in the form a circle" affect the overall performance of a circuit?

The effective resistance of a circular circuit can impact the overall performance of the circuit by affecting the flow of current. A higher effective resistance can result in a decrease in the amount of current flowing through the circuit, which can impact the functioning of the circuit as a whole.

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