# Are these two resistors in Parallel?

• jwllorens
In summary, the conversation discusses a circuit with resistors and wires, with a current source applied to points A and B. The question is whether the two green resistors are in parallel and can be reduced to a single resistor using (Ra*Rb)/(Ra+Rb). The expert confirms that this is possible and suggests using KCL or other techniques to analyze the circuit further. They also mention the possibility of using Delta-Y conversion for simplification.
jwllorens
Say I have a circuit that looks like this:

..._______
B___|_|_|_|___ A

The red and green lines are resistors.
The black lines are wires.

Assume a connection between any component line that is at a right angle to any other line, and a current source applied to points A and B.My question is this: Are the two green resistors in parallel, and thus, can I reduce them to a single resistor using (Ra*Rb)/(Ra+Rb)?

If not, any suggestions on how to calculate the equivalent resistance of this entire circuit, between points A and B?

jwllorens said:
Say I have a circuit that looks like this:

..._______
B___|_|_|_|___ A

The red and green lines are resistors.
The black lines are wires.

Assume a connection between any component line that is at a right angle to any other line, and a current source applied to points A and B.

My question is this: Are the two green resistors in parallel, and thus, can I reduce them to a single resistor using (Ra*Rb)/(Ra+Rb)?

If not, any suggestions on how to calculate the equivalent resistance of this entire circuit, between points A and B?

Welcome to the PF.

It's a little hard to read the diagram, but if there are just wires connecting the tops and bottoms of the two green resistors, then yes, they are in parallel.

berkeman said:
Welcome to the PF.

It's a little hard to read the diagram, but if there are just wires connecting the tops and bottoms of the two green resistors, then yes, they are in parallel.

I had to magnify the page to really see the diagram but they ARE black (lines) so your explanation is correct.

great, thank you. So the whole thing can be reduced to a diamond shaped circuit with a resistor in the middle, which becomes an irreducible circuit, at which point kirkoffs equations can be applied?

jwllorens said:
great, thank you. So the whole thing can be reduced to a diamond shaped circuit with a resistor in the middle, which becomes an irreducible circuit, at which point kirkoffs equations can be applied?

There may be other simplifications, depending on the values of the resistors (like if there are symmetries). But in general yes, you would use KCL or some other technique to work on the circuit at that point.

jwllorens said:
great, thank you. So the whole thing can be reduced to a diamond shaped circuit with a resistor in the middle, which becomes an irreducible circuit, at which point kirkoffs equations can be applied?

Irreducible is a bit strong, since simple circuits like that have been done and have equations you can look up. Google "Delta-Y conversion" to see what I mean. You have a delta and want a Y and then you can go from there.

These conversion were done USING kirchhoff analysis, so of course you CAN just do that.

## 1. What is a parallel circuit?

A parallel circuit is a type of electrical circuit where the components are connected in branches, allowing multiple paths for the current to flow. This means that the current is divided between the branches, and each component receives the same voltage.

## 2. How do I know if two resistors are in parallel?

If two resistors are connected to the same two points in a circuit, they are considered to be in parallel. This means that the current will have two or more paths to flow through, and the resistance of each resistor will have an effect on the total resistance of the circuit.

## 3. What is the total resistance of two resistors in parallel?

In a parallel circuit, the total resistance is calculated using the formula: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn, where R1, R2, R3, etc. are the individual resistances. This means that the total resistance will always be less than the smallest individual resistance.

## 4. How does a parallel circuit differ from a series circuit?

In a series circuit, the components are connected in a single path, meaning that the current must flow through each component in order. In a parallel circuit, the components are connected in branches, allowing for multiple paths for the current to flow. Additionally, in a series circuit, the total resistance is equal to the sum of all individual resistances, while in a parallel circuit, the total resistance is always less than the smallest individual resistance.

## 5. What are some common applications of parallel circuits?

Parallel circuits are commonly used in household and commercial electrical systems, as well as in electronic devices. They are also used in power distribution systems, where the current is split into smaller branches to reduce the load on each individual branch. Additionally, parallel circuits are used in light bulbs and holiday lights, as they allow for each individual bulb to receive the same voltage and continue functioning if one bulb burns out.

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