# Are these resistors in parallel?

I am self learning, this is not for a class, just for my own understanding because I am curious.

I think I have a fundamental misunderstanding of parallel resistors. The way I understand it, two resistors are in parallel if each resistor terminal connects to the same node. So, the example below shows RL in parallel with RON and then in series with RWIRE.

Based on the definition of parallel resistors, why isn't RON in parallel with RWIRE and then in series with RL? RON and RL both connect to the voltage source, but RON and RWIRE both connect to the capacitor in what appears to me to be in the same way.

A follow-on question: remove VS and RL so that you just have RON, RWIRE, and CGS2. Would RON and RWIRE be in parallel in that case? I would think so.

• It depends from which side you are looking at the circuit. From a voltage source point of view, we have R_ON in parallel with (R_wire + Cgs). But if you are looking from the capacitor point of view, the resistance seen by the capacitor (from capacitor terminals) is equal to R_ON||R_L +R_wire. Do you see the difference? electronics.stackexchange.com/questions/377467/…
– G36
Commented Dec 18, 2022 at 14:48
• I think so? Correct me if wrong: so, from the capacitor point of view, as a Thevenin equivalent, I would redraw the circuit without the capacitor in the diagram, leaving an open circuit in it's place, and then in that case, I could see that RTH = RL || RON + RWIRE. Likewise, from the voltage source point of view, as a Thevenin equivalent, I would remove the voltage source, leaving an open circuit in place of Vs, and then RTH = RON || RWIRE + RL ?
– pgk
Commented Dec 18, 2022 at 15:05
• You got it right. Good job.
– G36
Commented Dec 18, 2022 at 17:07

It might help if you think of Vs as having low (eg. zero) source resistance. .

Changes in voltage at the node indicated above (looking to the left in the direction of the green arrow, with respect to ground) would be opposed by by current changes in both Ron and RL as if they were directly in parallel.

So the Thévenin equivalent circuit of those three components results in a source resistance that is RL||Ron but the voltage is Vs*Ron/(RL+Ron).

• Thanks! I think this clears it up. These drawings came out of a text book. When I modeled this in SPICE it seems like the text book is correct, so I wasn't questioning the drawings. Basically my criteria for resistors in parallel isn't quite right. I feel like I was missing what you seem to be implying: the sum of the currents through each parallel resistor adds to the total current going into a junction where the current splits.
– pgk
Commented Dec 18, 2022 at 14:55
• Yes. Keep in mind the careful wording about changes in voltage. Commented Dec 18, 2022 at 15:12

There are no resistors in parallel in your circuit. Nor in series. Note that "parallel" and "series" are not the only options. There are many circuit configurations. The resistors in your circuit (a) are in a "T-network".

The way I understand it, two resistors are in parallel if each resistor terminal connects to the same node.

RL and RON do not meet that criteria. Only one node is shared by both resistors and therefore, they cannot be regarded as being in parallel.

Let me put a different spin on it.

two resistors are in parallel if each resistor terminal connects to the same node.

Let me rephrase. "Two terminal elements are in parallel if one terminal of the elements connect together at one node and the other terminal of the elements are connected together at a second node."

The main feature of elements (or branches) in parallel is that they have the same voltage across them. Not by chance but because they are parallel.

The circuit in Figure 1 has three parallel branches. None of the elements themselves are in parallel but the series combination of Vs and RL is in parallel with RON is in parallel with the series combination of Rwire and C.

To find the resistance seen looking back toward the source from elsewhere in the circuit, the contribution of the source to the total resistance must be included. Voltage sources (ideal) have an internal (series) resistance of 0 ohms. Current sources have an internal (parallel) resistance of infinite ohms. So for analysis, voltage sources are replaced with a short, current sources replaced with an open circuit. To find the Thevenin resistance seen by the capacitor looking back to the source, the circuit is modified as shown in Figure 2.

Clearly with the Vs replaced with a short, RL and RON are in parallel with Rwire in series with the combination.$$R_{Th}=R_{L}//R_{ON}+R_{wire}$$

To demonstrate how series/parallel can change with point of view, consider the total resistance, Rload, seen by the source for dc and low frequencies as shown in Figure 3. Here the source is removed to "see" what is connected. The capacitor looks like an open so it is also removed. RL and RON are now in series because there is no current in the third branch (Rwire has no effect).$$R_{load}=R_{L}+R_{ON}$$ They are in parallel from the Thevenin point of view.

From a high frequency point of view, the capacitor is replaced with a short as shown in Figure 4. Now Rwire is in parallel with RON. RL is in series with that parallel combination. $$R_{load}=R_{L}+R_{ON}//R_{wire}$$

simulate this circuit – Schematic created using CircuitLab

This question comes up here frequently. Two resistances are in parallel only if they're directly connected together at both ends. There can't be any other circuit elements in series with either of them before the connection. You know a formula for the equivalent resistance of parallel resistors and hope to use it for cases that don't quite fit that definition. It won't work. You can solve all of the problems of resistors and voltage or current sources with no formula except Ohm's law.

When current can take more then one path,the paths,and everything in those paths are parallel with the other paths. R wire and the capacitor are connected in series, together they are connected in parallel with R on. R wire and the capacitor, are connected in series with RL. Once the capacitor is fully charged,no more current flows through it or R wire Notice the path current takes, from its source, first it flows through RL, then it takes two paths. To better follow the flow of current, from its source, think of the capacitor as resistor.