# Any difference in parallel and row resistor circuit?

My goal is to create a 1.5 ohm resistor. I have 2 ohm and 1 ohm ones on hand. My idea was either to create two 3 ohm resistors to connect them in parallel or connect them in row. See picture below for better explanation. Is there any difference which one I choose?

For me both seem to give the same result of 1.5 ohms, but is there any other things that differ?

• In theory, the best way to see that these are exactly the same is to realize that in case #2 the voltage present at the two nodes between the series connected resistors (above and below) will be the same and so the bridge wire in case #1 will carry no current. In practice, you may want to think about what happens if a single resistor is accidentally destroyed or bridged by a screwdriver, for example.
– jonk
Jul 28 at 5:43

There is no difference in the electrical behaviour. This is because the extra wire is bridging two nodes that are at the same voltage. This means it doesn't change the characteristics of the circuit.

If there is a failure mode of concern where a resistor shorts or one opens, then there might be a preference for one or the other; but this depends on the likely failure mode and the preferred behaviour.

The added center wire would have no net effect since the two resistor dividers are equal, (same voltage at the center, so there's no current flow).

• Of course with real resistors and their tolerances there will most likely be some small mismatch.
– Nedd
Jul 28 at 5:54

Short answer: For ideal components, both topologies are equivalents.

Long answer: For real components, there are a few differences regarding some aspects:

1. As @jp314 highlighted, there are differences in reliability and many aspects should have to be taken into account to decide which is better. For instance, if it is desired to keep an electrical path in this branch in the case of an open fail resistor, option 1 is a wise choice for 2 components failure case (circuits keep functional in case a single component fails on both topologies and both fail in case of 3 components fail). Moreover, the expected value and the variance for total resistance may be different for both topologies in the cause of failure in a single or multiple components. That leads us to a second aspect:
2. Total resistance $$\R_{tot}\$$ statistical distribution is different for these topologies. For instance: Assuming that those resistors have values given by a normal gaussian distribution $$\\mathcal{N}(R_{n},{(tolerance \cdot R_{n})}^{2})\$$, (where $$\R_{n}\$$ is the nominal value for a resistor) series association differs from a parallel association for total resistance $$\R_{tot}\$$ expected value $$\E(R_{tot})\$$ and variance $$\Var(R_{tot})\$$.

Thus, in real world, these topologies are not equivalent.

• agreed, so which configuration has the higher precision?
– Jens
Jul 28 at 20:23
• Topology 1 has better precision. Topology 2 has better accuracy. Jul 28 at 20:30

You don't need four resistors and you don't need 2 Ohm.

simulate this circuit – Schematic created using CircuitLab