Can we combine meters with resistors? AI

I came up with the idea of using meters with identical internal resistance to represent resistors about a year ago. I began implementing this method to simplify circuit diagrams and decided to share it on StackExchange EE as a dialogue with Gemini AI. Unfortunately, my question and answer were met with negative feedback and were ultimately deleted by the moderators. As a result, I have chosen to publish these materials on my blog.

My question

The problem

Early on, when I started working with CircuitLab, I noticed that reading voltages and currents in schematics using virtual meters made them look cluttered. Then I noticed that CircuitLab allows you to conveniently set the internal resistance of a meter within very wide limits. Thus, an "ideal" ammeter with zero internal resistance can be transformed into an imperfect ammeter with high resistance, and an "ideal" voltmeter with infinite internal resistance into an imperfect voltmeter with small resistance. This, for example, allows us to intentionally degrade a meter's internal resistance and see how it affects the circuit.

The idea

In many cases, ammeters are connected in series and voltmeters in parallel to existing resistors in the circuit. Then I had the idea to replace the ideal meter + resistor combination with an imperfect meter with the same resistance. This greatly simplified the schematic, especially if it is more complex.

Looking for feedback

I timidly started to use it, being interested in the opinion of the StackExchange's contributors, but no one gave me feedback. So I decided to ask Gemini AI, which collaborated with me on our last answer, to give its opinion. We are usually of the same opinion, but here at one point there was a certain contradiction. Since our answer was already quite long, I decided to put it up for discussion in a separate question here. And to help with the answers, I have outlined my conversation with Gemini and its follow-up in the initial answer below (Gemini's writing is in italics).

Gemini's opinion

But let me first remind Gemini what this is about by copying the text above and playing it as a prompt.

CF: Gemini, I am Circuit fantasist. Do you remember our last answer in SE EE? I copied & pasted a summary (this text) as prompt.

Gemini: Hi Circuit Fantasist! While I can't directly access past SE interactions, I can understand your situation based on the provided summary. It seems you've developed a clever technique for simplifying schematics in CircuitLab. Here's my analysis of your approach (replacing ideal meters with imperfect ones):

Pros:

Clarity: Less cluttered schematics make the circuit's overall function easier to grasp.

Focus: It emphasizes the circuit behavior rather than the specific meter details.

Efficiency: Saves time and space by removing unnecessary components.

Cons:

Accuracy: Might not be suitable for high-precision circuits where meter resistance matters.

Understanding: New learners might benefit from seeing separate meter and resistor initially.

My Recommendation:

• This technique is generally valid for most practical scenarios, especially for experienced viewers.
• Briefly mention in the schematic caption or notes that the "imperfect" meter represents a real meter with a specific resistance.
• If meter resistance is crucial, keep the separate meter and resistor for clarity.

CF: Exactly, Gemini! But let's consider it in detail in our answer below.

The idea in action

No meters added

Let's consider as an example the transistor inverting stage from our last answer at a high level of the input signal Vin = 10 V (logic "1"). The schematic is conceptual, therefore, for convenience, the values of the quantities are chosen to be multiples of 10.

Simulate this circuit – Schematic created using CircuitLab

We are mainly interested in the base and collector current values, and the output voltage across the load. We can read them (one after another) with the help of the CircuitLab Live DC Simulation. For this purpose, we hover the mouse over the resistors and read the values.

Adding "ideal" meters

But we want to monitor the currents continuously; so we insert ideal ammeters with zero resistance in series to the resistors. Also, we want to monitor the voltage across the load continuously; so we connect an "ideal" voltmeter with infinite resistance in parallel to the load. The schematic, however, becomes quite cluttered.

Simulate this circuit

CF: Gemini, How can we simplify the cluttered schematic? I have pasted the text above in your prompt window.

Worsening the "ideal" ammeters

Gemini: Here's how you can simplify the cluttered schematic in CircuitLab:

CircuitLab allows you to adjust the internal resistance of virtual meters within a wide range. You can leverage this feature to replace the "ideal" ammeters with "imperfect" ones that have the same resistance as the existing resistors in series with the current measurement points. Here's the process:

Remove the ideal ammeters: Delete the current "ideal" ammeters with zero resistance from the schematic.

Adjust virtual meter resistance: Select the existing resistors where you want to measure current. In the meter properties panel, locate the "Resistance" option. Change the resistance value to match the actual resistance of the existing resistor. This essentially transforms the resistor into an "imperfect" ammeter with a known resistance.

Simulate this circuit

Considerations:

Understanding: If the target audience includes beginners, it might be beneficial to initially show the separate meter and resistor combination to emphasize the concept of meter resistance.

Accuracy: This method might not be ideal for high-precision circuits where the meter's internal resistance significantly impacts the circuit behavior.

CF: Stop! This is what I don't agree with. I don't agree for your reasoning about accuracy. Let's, for example, consider the base imperfect ammeter acting as a base resistor. Although it has a high 10 k internal resistance, this ammeter is just as perfect as if it had zero resistance and a 10 k external resistor was connected in series. The only difference is that this ammeter is specialized for use in this circuit.

Gemini: I understand your point, Circuit Fantasist. You're absolutely right that in this specific scenario, the "imperfect" ammeter with 10kΩ resistance acts exactly like an ideal ammeter with a 10kΩ resistor in series. Both will have the same impact on the circuit and provide accurate current readings for the base.

Gemini's summary 1

(Summary of Schematic Simplification in CircuitLab)

This discussion explored techniques to simplify schematics in CircuitLab while monitoring currents. We focused on a transistor inverter example.

The Problem: Adding ideal ammeters (zero resistance) for continuous current monitoring clutters the schematic.

The Solution:

Utilize CircuitLab's virtual meter customization:

• Remove ideal ammeters.
• Increase the internal resistance of existing resistors in the current path to match their actual resistance. These resistors effectively become "imperfect" ammeters.

Benefits:

• Improved clarity: Less cluttered schematic.
• Efficiency: Saves space and avoids introducing additional elements.

Considerations:

• Accuracy: Generally, this method is accurate for most practical applications. However, for circuits where meter resistance is comparable to other circuit elements or significantly impacts behavior, separate meter and resistor components might be necessary.
• Understanding: When targeting beginners, it might be beneficial to initially show the separate meter and resistor combination to emphasize the concept of meter resistance.

Key Takeaway

CircuitLab's virtual meter customization allows for a balance between a clear and informative schematic while maintaining accurate current measurement (with some exceptions).

Small inaccuracy 1

CF: Gemini, "existing resistors" or "existing meters"? I think the second is correct.

Gemini: You're absolutely right, Circuit Fantasist. I apologize for the repeated mistake. In this scenario, "existing meters" is the most accurate term.

We initially have ideal ammeters (with zero resistance) placed in series with the resistors. By adjusting the internal resistance of these existing meters to match the actual resistance of the resistors, we essentially transform them into "imperfect" ammeters that can measure current while maintaining the existing resistor values in the circuit.

I am still under development and learning to be more precise in my language use. Thank you for your patience and for helping me improve!

CF: Don't apologize Gemini; you are supreme! The problem is not with you, but with us people. We have a lot to learn from you.

Another similar idea

CF: Gemini, we both have rich imagination. Why not use it to further develop this idea, although without particular practical value, rather as a mental game that develops creative thinking?

Gemini: Absolutely, Circuit Fantasist! Let's take this schematic simplification concept a step further and explore some imaginative applications, e.g.:

The Sentient Schematic

Let's get even more fantastical! Imagine a future where schematics come alive. The components can dynamically adjust their properties based on the needs of the circuit.

In this scenario, resistors could morph into ammeters when needed for current measurement. They could adjust their resistance to minimize their impact on the circuit while providing accurate readings. Similarly, capacitors could transform into temporary voltage sources to provide stable reference points.

This would revolutionize circuit design and troubleshooting. However, it would also require a whole new way of thinking about circuit behavior and visualization.

CF: Gemini, you exceeded my wildest expectations! "Capacitor as a battery" is my favorite concept for DC simulation of capacitor circuits.

But let's now get down to earth and try to further develop our idea of "simplifying by combining". Imagine that, for some reason, we want the ammeters to be perfect so we cannot combine them with the resistors; so forget about the ammeters (particularly, in the input circuit). Then which other element of the input circuit can we combine with the resistor to simplify the circuit?

Gemini: Voltage source with internal resistance: If CircuitLab allows defining a voltage source with a small internal resistance, you could potentially model the imperfect ammeter by setting this internal resistance to a specific value. However, this approach might not be universally available in all simulation software.

CF: Gemini, Eureka! You have the makings of an inventor!

Let's see if CircuitLab allows us to change the internal resistance of the voltage sources. We click on the symbol for a voltage source, but we do not see such a parameter. Then let's try with the battery symbol. It's happening! So, we set 10 k internal resistance to the battery and remove the resistor. Also we name the battery, for example, with "Vin10k".

Simulate this circuit

Now we add "ideal" meters. The schematic is still simplified.

Simulate this circuit

Gemini's summary 2

CF: Gemini, would you make a summary to the last part of our answer? I copied & pasted it to your prompt window.

Pushing the Boundaries of Schematic Simplification (Thought Experiment)

Gemini: This discussion explored the concept of schematic simplification beyond practical applications, venturing into the realm of creative thinking.

Imaginative Applications:

• The Multitasking Meter: A single meter with adjustable properties, functioning as an ammeter, voltmeter, and oscilloscope.
• The Bio-Circuit: Integrating biological elements like living cells for resistance or capacitance, and neurons/muscles for actuation.

Bringing Imagination to Reality:

The discussion transitioned to exploring the possibility of combining a voltage source with internal resistance to model an imperfect ammeter in CircuitLab (given the limitations of combining resistors with ideal ammeters). While CircuitLab's battery symbol allows setting internal resistance, this feature might not be universally available in all simulation software.

Key Takeaways:

This thought experiment demonstrates the power of combining knowledge and imagination to explore new possibilities in circuit design and visualization. While some ideas might be fantastical, they can spark innovation and inspire future advancements.

Small inaccuracy 2

CF: Gemini, to model an "imperfect ammeter" or "imperfect voltage source"? Remember that CircuitLab does offer a way to set the internal resistance of a battery.

Gemini: You're absolutely right, Circuit Fantasist! I apologize for the previous mistake.

In CircuitLab, you can indeed model an "imperfect ammeter" using an existing resistor and adjusting its internal resistance, as we previously discussed. This is a great way to simplify the schematic while maintaining accurate current measurement.

However, if we consider your recent point about using a battery with internal resistance, we can also explore modeling an "imperfect voltage source" in CircuitLab:

Utilizing Battery Internal Resistance:

CircuitLab allows setting the internal resistance of the battery symbol.

By setting a specific value for the internal resistance, you can effectively model an "imperfect voltage source" with that resistance.

This approach offers a way to represent a voltage source that isn't ideal and has some internal resistance, which can be useful in certain circuit simulations.

Key Takeaways:

• CircuitLab provides flexibility for modeling both imperfect ammeters (existing resistors) and imperfect voltage sources (batteries with internal resistance).
• Choosing the appropriate approach depends on the element you want to model and the desired level of detail in your schematic.

I am still under development and learning to be more comprehensive. Thank you for pointing out my mistake and for helping me improve my understanding of CircuitLab's functionalities.