# Resistors both in series and in parallel?

Consider this circuit. I'm assuming that the resistors have the same resistance. The same amount of current flows through them so they must be in series. But the voltage across each resistor is also the same so they must be in parallel. So are these resistors connected in series or parallel?

Am I just confusing the definitions?

• They're in series. If they're the same resistance then they'll have the same voltage across them but that does not automatically mean it has to be parallel. Any 2 random resistors in the world that happen to have the same voltage across them are not necessarily in parallel. Jul 27 '21 at 23:37
• Series. ........ Jul 27 '21 at 23:37
• @Unimportant So what needs to happen for them to be in parallel then? Jul 27 '21 at 23:41
• Why do you think they have the same voltage across them? Don't confuse a pictorial representation (where y = voltage) with nodal analysis Jul 27 '21 at 23:42
• @PTSONIC To tell if something is in parallel, just put your pencil point down onto one of the parts in a schematic, call this the starting part, and see if you can find a way to trace out through one end or the other of the starting part and make the pencil only follow along the wires, to go through one other part. And after coming out the other end of that second part, find a way back to your starting part entering at its other end and do all this without lifting the pencil from the paper or going through a third part to get there. If so, they are in parallel.
– jonk
Jul 28 '21 at 1:56

the voltage across each resistor is also the same

No.

The voltage across the total of both resistors is the same no matter their values (assuming the voltage source can provide sufficient current).

The voltages across each of the two resistors are the same ONLY if the two resistors are of equal value. If not, the voltage across each resistor is proportional to its value, per Ohm's Law.

In general, circuits are about galvanic closed loops. You can select any such loop you want.

Here's a GRANU schematic (generally recognized as not useful):

simulate this circuit – Schematic created using CircuitLab

A galvanic closed loop might be $$\R_1\$$, $$\C_4\$$ and $$\B_1\$$, for example. You can draw a circle over that to form a loop. Another loop might be just $$\C_1\$$ and $$\R_4\$$. Another loop might be $$\C_2\$$, $$\R_5\$$, $$\R_4\$$, and $$\R_3\$$, since those are also all connected and if you ignored all the other parts and wiring would form a loop. There are many loops above.

But there aren't many parallel pairs of parts. $$\C_1\$$ is in parallel with $$\R_4\$$, $$\C_3\$$ is in parallel with $$\R_6\$$, and $$\C_4\$$ is in parallel with $$\R_7\$$. That's because in all three cases there is a loop formed only by those two parts. If you cannot find a loop that involves just the two parts, then they are not in parallel with each other.

Now let's look at a different schematic:

simulate this circuit

Both resistors have the same voltage across them. But they are not in parallel with each other. Having the same voltage across a part does not mean they are in parallel. And not only do both those resistors have the same voltage across them, but they also have the exact same voltages on both ends, too. Yet they are not in parallel because you cannot draw a loop through just those two resistors. It cannot be done.

If, however, you strung a wire from the top end of one resistor to the top end of the other resistor, then they'd be in parallel.

They are in series because current flows through one and then the other. The fact that the voltages and currents are equal are effects of parallel/series connection but don’t define it.

• Your language here is contradictory. You say "series because current flows through one and then the other" but in the next sentence say "The fact that...currents are equal...are effects of parallel/series connection but don't define it". By definition, the current through two elements in series must be the same. Jul 28 '21 at 13:04
• The definition is based on the effective electrical arrangement, where the electrons go is a side-effect of this. That becomes relevant in a more complex scenario where, as is typical, one or more other components are added at the junction of the two resistors- the base of a BJT for example. In that scenario the resistors would be considered to be in series but the currents are no longer identical.
– Frog
Jul 28 '21 at 19:45
• If the currents are not exactly the same then the elements are not in series. If more than two elements are connected at the same node then those elements are not in series. As much as I hate to quote Wikipedia: "The electric current in a series circuit goes through every component in the circuit. Therefore, all of the components in a series connection carry the same current." Jul 28 '21 at 20:59