Finding Effective Resistance Across A Hexagon: A Homework Solution

In summary, the question asks for the effective resistance across points A and B in a regular hexagon circuit with resistances of r each. The solution involves simplifying the circuit by collapsing the horizontal line into a point and finding combinations of resistors in series or parallel. The potential is the same across points connected by a wire, and there are four pairs of parallel connections in the simplified circuit.
  • #1
Asphyx820
10
0

Homework Statement



The diagram represents a regular hexagon. The resistances are r each
Find the effective resistance across points A & B

http://tinypic.com/r/153n39d/7


Homework Equations





The Attempt at a Solution



A resistance less wire passes through one of the diagonals. so can we remove the wire and then solve.
i tried but i didnt get the answer.
do none of the points have same potential
 
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  • #2
What exactly do you mean by "remove the wire"? You can't just erase it because that would create more nodes than the original circuit has (all points connected by unbroken wire conductor belong to same node).
 
  • #3
Asphyx820 said:
A resistance less wire passes through one of the diagonals. so can we remove the wire and then solve.
i tried but i didnt get the answer.
Show what you did.

I assume that when you "remove the wire" you mean that points connected by the wire can be joined. Do that and look for combinations of resistors in series or parallel that can be replaced by their equivalent. Step by step you can simplify this arrangement.
 
  • #4
Try redrawing the circuit after you collapse the horizontal line into a point. [edit: what Doc said :redface:]
 
  • #5
Ok ! so what do I do?
I can't find any points having same potential. how will i simplify the circuit?
 
  • #6
Asphyx820 said:
Ok ! so what do I do?
I can't find any points having same potential. how will i simplify the circuit?
:confused: Points connected by a wire have the same potential.
 
  • #7

Related to Finding Effective Resistance Across A Hexagon: A Homework Solution

1. What is the purpose of finding effective resistance across a hexagon?

The purpose of finding effective resistance across a hexagon is to determine the overall resistance of a circuit or network that is arranged in a hexagonal shape. This is important in understanding the flow of electricity through the circuit and can help in designing more efficient and effective electrical systems.

2. How is effective resistance across a hexagon calculated?

The effective resistance across a hexagon is calculated using a formula that takes into account the individual resistances of each component in the circuit as well as the arrangement of the components in a hexagonal shape. This formula can be derived using Kirchhoff's laws and Ohm's law.

3. What factors can affect the effective resistance across a hexagon?

The factors that can affect the effective resistance across a hexagon include the individual resistances of the components in the circuit, the arrangement of the components in a hexagonal shape, and the type of material used for the components. Other factors such as temperature and humidity can also have an impact on the resistance.

4. Can the effective resistance across a hexagon be reduced?

Yes, the effective resistance across a hexagon can be reduced by using components with lower resistances, adjusting the arrangement of the components, or using materials with higher conductivity. However, it is important to consider other factors such as cost and practicality when making these changes.

5. How is the effective resistance across a hexagon useful in real-world applications?

The effective resistance across a hexagon is useful in real-world applications as it can help in designing more efficient and effective electrical systems. This can lead to cost savings, improved performance, and better reliability. It is also important in analyzing and troubleshooting existing circuits to identify potential issues or areas for improvement.

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