# Circuits: Draw Equivalent Resistance

In summary, The person is struggling with simplifying a circuit and is unsure of how to relate certain resistances. Another person helps them by suggesting to combine the resistances in parallel and explains why they are in parallel. The original person thanks them and another person clarifies that parallel means both ends of the resistors are connected together and the current splits between them.

## Homework Statement

Man, I stink at circuits. I have to simplify the 1st circuit in the image below to an equivalent resistance. I am almost there, but I am unsure of how to relate the remaining 3 resistances. In the drawing, a subscript Ri||j denotes the equivalent resistance of the two parallel resistors i and j; similarly, Ri+j is the equivalent resistance of the two series resistors i and j.

Now, I am not sure how to relate $R_1,\,R_{(3||4)+5},\,R_2$ and I think my confusion lies in the fact that I do not know what is going on with the current in this last circuit. Can someone help me out with that?

You have it pretty well finished! Just combine the R(3||4)+5 with the R2 in parallel. That result is in series with R1.

Delphi51 said:
You have it pretty well finished! Just combine the R(3||4)+5 with the R2 in parallel. That result is in series with R1.

OK! Now, this is because after the current leaves R1, it splits among R2 and R(3||4)+5 so we combine them in parallel. Right?

Thanks again Delphi!

They combine in parallel because they *are* in parallel! Look at how their leads connect.

gneill said:
They combine in parallel because they *are* in parallel! Look at how their leads connect.

I think you are both saying the same thing! Parallel means both ends of the resistors are connected together AND that the current splits between them.

## 1. What is equivalent resistance in a circuit?

Equivalent resistance is the combined resistance of multiple resistors in a circuit. It is the single resistor that would produce the same amount of resistance as all the resistors in the circuit combined.

## 2. How do you calculate equivalent resistance?

To calculate equivalent resistance, you can use the formula 1/R(total) = 1/R1 + 1/R2 + 1/R3 + ..., where R(total) is the equivalent resistance and R1, R2, R3, etc. are the resistances of each individual resistor in the circuit.

## 3. What is the purpose of finding equivalent resistance?

Finding equivalent resistance allows us to simplify complex circuits and make calculations easier. It also helps us understand the overall behavior of a circuit.

## 4. Can equivalent resistance ever be greater than the individual resistances?

No, equivalent resistance can never be greater than the individual resistances. It can only be equal to or less than the smallest resistance in the circuit.

## 5. How does the arrangement of resistors affect equivalent resistance?

The arrangement of resistors in a circuit can affect the equivalent resistance. In series circuits, the equivalent resistance is the sum of all the individual resistances. In parallel circuits, the equivalent resistance is less than the smallest individual resistance.

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