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Tolya
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We have an infinite net of regular hexagons. Each side of hexagons has a resistance R. What is the resistance between two opposite vertexes of hexagon(s)?
Tolya said:This is a misunderstanding. :) I have already solved this problem. I was only trying to represent it to the people, who are interested in it. But I suppose I wrote this problem in the wrong forum section... Dick, please, if you have the answer, write me a private message. We'll check the result ;)
Tolya said:If it so easy for you, please, write me your answer :) We will check.
Dick said:That's a variation on an old problem with an infinite net of squares. Picture pushing 1 amp into the circuit at a vertex and taking it out at infinity. 1/3 amp flows through each resistor away from the vertex. Then forget that and picture taking 1 amp out of the circuit and feeding it in at infinity. Now we have 1/3 amp flowing through each resistor into the vertex. Now add the two, putting the 1 amp in at one vertex and taking it out at an adjacent one. Now the total going to infinity is zero, there is a total of 2/3 amp flowing through the connecting resistor and a total of 1 amp flowing between the two vertices through the whole network. What's the voltage across the two vertices? What's the total resistance?
Avodyne said:
A resistor is an electrical component that is used to restrict the flow of current in a circuit. It is typically made of a material with high resistance, such as carbon or metal, and is designed to dissipate heat generated by the flow of electricity.
Resistors restrict the flow of current by creating resistance in a circuit. This resistance slows down the flow of electrons and can help control the amount of current in a circuit.
When current flows through a resistor, it encounters resistance, which causes some of the electrical energy to be converted into heat. The more resistance a resistor has, the more heat it will generate.
The resistance of a resistor can be calculated using Ohm's Law, which states that resistance (R) is equal to the voltage (V) divided by the current (I). This can be expressed as R = V/I. The unit of resistance is ohms (Ω).
Some common problems with resistors include overheating, which can lead to malfunction or failure, and incorrect resistance values, which can cause issues with the functioning of a circuit. It is important to choose the right type and value of resistor for a particular circuit to avoid these problems.