In a simple circuit with a single resistor the entire voltage provided by the cell drops. It is independent of the resistance. Why does this happen? What is the mechanism behind this? I mean why does not it vary with varying resistances.
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1$\begingroup$ If you jump off a wall, do you have to fall all the way down? $\endgroup$– Jon CusterCommented Sep 6, 2017 at 19:50
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$\begingroup$ @JonCuster I mean why all the voltage(energy) is used up by the resistance. Cant it travel towards the negative terminal? What happens when there is no resistance and the connecting wires ideally dont have any resistance at all? $\endgroup$– Amyanshu JenamaniCommented Sep 6, 2017 at 19:56
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1$\begingroup$ The electron was lifted up from the negative terminal to the positive terminal. It has to return to the negative terminal. It has to fall all the way back down. $\endgroup$– Jon CusterCommented Sep 6, 2017 at 19:58
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$\begingroup$ @JonCuster That would mean in a circuit with no resistance the current will flow forever......Is that right? $\endgroup$– Amyanshu JenamaniCommented Sep 6, 2017 at 20:02
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$\begingroup$ @JonCuster This is a good analogy, but it assumes the circuit is in equilibrium (equivalently, it assumes there exists some time independent V in the circuit). But I think a lot of confusion over this comes from people not understanding how circuits get to their equilibrium. $\endgroup$– Jahan ClaesCommented Sep 6, 2017 at 20:06
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1 Answer
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It might be helpful to think about what would happen if the voltage drop in the resistor was not equal to the voltage gained in the battery. In this case, each time an electron traveled around the circuit, it would gain kinetic energy, since it would gain more energy from the battery than it lost passing through the resistor. Thus, the current would increase. But the increase in current would cause the voltage across the resistor to increase. Eventually, the current would increase to the point that the voltage across the resistor would equal the voltage of the battery.
When people say that the voltage around a circuit has to add up to zero, they're talking about circuits in equilibrium. You can see that if the voltages didn't add to zero, that would make the current change so that they do add up to zero. That's why we can assume an equilibrium state exists.
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$\begingroup$ How the current would increase? Can u explain the route of the electron around the circuit and the energy change associated with it more clearly? $\endgroup$ Commented Sep 6, 2017 at 20:24
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$\begingroup$ @AmyanshuJenamani The electron goes through the battery. This increases its kinetic energy by $eV$, where $V$ is the voltage of the battery. Then it goes through the resistor. This decreases its kinetic energy by $eV_R$, where $V_R$ is the voltage across the resistor. If $V>V_R$, then the total change in kinetic energy is $e(V-V_R)>0$, so the electron gained kinetic energy after going around the circuit once. Thus, it's increasing the current. $\endgroup$ Commented Sep 6, 2017 at 21:05