This post describes some conceptual errors with voltage sources, that arise from the definition of voltage source and short circuit.
Voltage sources and short circuits
As explained in this post, a voltage source imposes a voltage difference across two points, as shown in figure 1. This means that, between points A and B, there is a voltage difference of x volts.
Figure 1 – Voltage source.
On the opposite side, a short circuit between two points means that those points are at the same voltage. As shown in figure 2, points A, C and D are at the same voltage level, but points A and B are at different voltage levels. So, when we draw a line connecting two points in a circuit, those points and all the intermediate points across that line are at the same voltage level.
Figure 2 – Representation of short circuit between points.
Shorting a voltage source
Keeping in mind what we stated before, shorting a voltage source, as shown in figure 3, is a physical impossibility. If we could short a voltage source, it would mean that there was a voltage difference of x volts between A and B (because of the voltage source), and simultaneously that A and B would be at the same voltage level (because of the short circuit), which is impossible!
Figure 3 – Conceptual error of shorting a voltage source.
Although shorting a voltage source is a conceptual error, there is nothing that prevents us from putting a conductive wire between the two terminals of a battery, which is what we typically call a short circuit.
Nevertheless, we need to take into account that there are no perfect voltage sources and there are no perfect conductors. This means that, in the real world, every wire that we use will have a small resistance, which is typically negligenciable for normal application circuits, but is indeed a resistance. Also, every voltage source that we use has a small internal resistance. So, if we consider this real scenario, the corresponding schematic is shown in figure 4. As we can see, we are no longer shorting a voltage source.
Figure 4 – Representation of a real voltage source, with internal resistance Rsrc, and a real conducting wire, with resistance Rcnd.
By applying Ohm’s Law, we get:
Taking into account the previous equation and that Rsrc and Rnd are very small, we can conclude that the voltage source will need to supply a very large current. Since real voltage sources can only supply a limited amount of current, crossing that threshold will lead to the increase of heat and ultimately the destruction of the device. So, although it’s not a conceptual error to short a battery with a wire, it’s still a bad idea 🙂