# How do I find the equivalent resistance of a circuit with a node between each resistor?

I can't make out what's in series and what's in parallel in this circuit.

The solution I've thought of so far is to consider R1 in series with R4 and R2 in series with R5. Then, (R1+R4), R3 and (R2+R5) would be in parallel and their resultant resistance would be in parallel with R6. I'm not entirely certain this solution is correct though.

A nudge in the right direction would be appreciated. • CircuitLab saves editable schematic inline with your post. No need for screengrabs. Press R to rotate a component. – Transistor Jan 26 '18 at 10:42
• And you have to look over the resistor values. – MatsK Jan 26 '18 at 12:39

## 2 Answers

Keyword Y-Δ-transformation:

You can transform the Y-configuration at R3, R4, R5 into a Δ-configuration Ra, Rb, Rc and then see that there are three parallel configurations (R1 || Ra, R2 || Rb and R6 || Rc) which can be simplified. simulate this circuit – Schematic created using CircuitLab

The answer depends on a couple of things that you don't have included in your question.

1. Is your source AC or DC? The symbol is telling me DC, but the 120V is suggesting that the question refers to AC. Whether your are direct or alternating determines the direction the little electrons will be swimming, which becomes relevant for the second part of this answer.
2. The answer is dependent upon the relative proportions. Roughly speaking, if R2 is really big as compared to R5, DC current will flow up from ground and flow right to left through R3. Conversely, if R5 is very large as compared to R2, the current will go left to right. Once you know that direction, this becomes an easy problem. (In an AC situation, you would [edit also need to] consider current to flow in the from V+ to ground, and would need to consider R1 and R4 as they relate to the rest of the circuit) 