# Does an ideal voltage source go against Kirchhoff's voltage law?

Very new to electronics. Stuck on this topic: In a circuit with zero resistance an ideal voltage source of example 5 volts will produce 5 volts, since ideal voltages don't have an internal resistance. But does that not go against Kirchhoff's voltage law that the sum voltage of a closed circuit should be zero? In this example with no resistance the sum will be 5 volts and not zero. What am I misunderstanding?

• Yes, all these "idealities" are contradictory. Like an infinitely strong wall being hit by infinite force. Commented Jan 13, 2022 at 18:59
• You're talking about shorting out an ideal voltage source, which also implies infinite current. Things break down when you start using ideal models in contradictory situations. Commented Jan 13, 2022 at 19:00
• Does this answer your question? Different and opposing voltage sources? Commented Jan 13, 2022 at 19:59

It does not lead to a contradiction in circuits where KVL is still applicable. KVL states that the voltage around a loop shall be zero, and a simple circuit where this model is useful looks like this:

simulate this circuit – Schematic created using CircuitLab

and indeed, the voltage around the loop is zero - there's a voltage drop of 5 V across the load.

There is a KVL contradiction when you apply a short-circuit to the ideal voltage source, or if you connect two different-valued voltage sources to the same nodes. These are artificial contradictions, simply because you've chosen an oversimplified model (ideal voltage sources and/or ideal short circuits). This does not mean that the model is universally bad, since it still held well when we had a real load, but it does mean that the model has limitations.

These are not the only types of problems with KCL/KVL. For example, when your wires are long enough compared to the wavelength of high-speed signals, KCL/KVL are unable to model certain electromagnetic effects that occur (example).

It's not exactly a violation of KVL. Consider what happens if the two supply terminals are connected by a resistor with zero resistance, which is what you are doing. Then the current through the resistor will be infinite, and you can use Ohms' Law to say that e = iR becomes 5 = infinity x 0.

Well, that is certainly true, in the sense that infinity = 5/0, but it's the sort of thing that leads to problems. There are methods for dealing with divide-by-zero situations, but at this point in your educations don't even go there.

So the rule with KVL and a voltage source is never to use a resistance of zero, and never use a current source with an infinite resistance.