Recently I was playing around with this circuit simulation, and I found that if I had a circuit with just a lightbulb and cell, then If I were to measure the voltage between the bulb and cell it gives me 0. But when I measure the voltage between both ends of the bulb it gives me the battery voltage. If the voltage was 0 for the first one, then how do electrons even move if there is no potential difference? I'm quite confused.
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$\begingroup$ The simulation assumes a superconducting wire and thus the potential difference across it is often ignored. Due to the idealisation that E=0, which is not true if there is a battery connected. It is just an abstraction. Which isn't what actually happens in superconducting wires, but the PD across them compared to the bulb is miniscule so is ignored. Conceptually, the simulation is entirely wrong. $\endgroup$– jensen paullCommented Jul 10, 2022 at 13:11
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$\begingroup$ @jensenpaull That's a bit harsh. Conceptually, the simulation captures the subset of the physics it's meant to capture. The drift current in the wire is not in that subset. But that, of course, is why students should do more with real wires and resistors before attempting simulations and mathematical abstraction. $\endgroup$– John DotyCommented Jul 10, 2022 at 13:26
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$\begingroup$ Except it has led OP to think that even in superconducting wires, the pd across them is zero. Which is wrong $\endgroup$– jensen paullCommented Jul 10, 2022 at 13:39
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$\begingroup$ @jensenpaull simulators aren't (for the most part) designed to teach students. For example, they also don't capture self heating behavior, arcing due to over voltage, interference due to proximity with other circuits, manufacturing variation between components, etc. $\endgroup$– The PhotonCommented Jul 10, 2022 at 15:04
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2 Answers
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In a real circuit, with a sufficiently sensitive voltmeter, you can measure a small voltage between the ends of a wire carrying current in a circuit like this. But, the wire is made of a low resistance material (commonly copper), so the voltage required to drive the current is small. This is by design.
The simulator idealizes this to zero resistance, so in simulation there is no voltage required to drive the current.
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If the voltage was 0 for the first one, then how do electrons even move if there is no potential difference?
For some reason this is a very common misconception. Electrons do not require a potential difference to move. They can and do move without a potential difference or even against a potential difference.
The potential difference across a resistor is proportional to the current through it. But that is not a general law of physics. Ohm’s law specifically applies to resistors, not to other materials or devices, such as batteries, capacitors, inductors, and superconductors. For all of those other devices current can flow without or even against a potential difference.
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$\begingroup$ Common wire materials are well modeled as ohmic. Ohm's law applies to them. $\endgroup$ Commented Jul 10, 2022 at 1:09
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$\begingroup$ It is a simulation, not a wire. In the simulation there is no voltage and there is no law of physics that requires there to be one. I often work with superconducting wires $\endgroup$– DaleCommented Jul 10, 2022 at 2:39
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$\begingroup$ Yes, it's a simulation. That's the real reason. In the real world, there would be a voltage between the ends of the wire. Ohm's law does not specifically apply to resistors: things that aren't officially resistors sometimes still follow Ohm's law. Be real: have you ever used superconducting wire to connect a cell to a light bulb? $\endgroup$ Commented Jul 10, 2022 at 2:50
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$\begingroup$ Yes, be real. The student has a real conceptual challenge and you are ignoring it. That the simulation is an approximation is a triviality, and that a real voltmeter has limited sensitivity is another. The conceptual mistake that the student is making is the common but incorrect idea that charges only move down a potential gradient. That is false in batteries, capacitors, inductors, and superconductors. You really do the student a disservice by ignoring their real conceptual challenge $\endgroup$– DaleCommented Jul 10, 2022 at 4:25
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$\begingroup$ I think that bringing up exotica like superconductors does nothing to help with the conceptual challenge here. When Ohm's law suffices, which it does here, it's a really good place for students to start. The real circuit uses an ohmic wire. The simulation isn't real. $\endgroup$ Commented Jul 10, 2022 at 11:23