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?

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    \$\begingroup\$ Yes, all these "idealities" are contradictory. Like an infinitely strong wall being hit by infinite force. \$\endgroup\$
    – Eugene Sh.
    Commented Jan 13, 2022 at 18:59
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    \$\begingroup\$ 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. \$\endgroup\$
    – Hearth
    Commented Jan 13, 2022 at 19:00
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    \$\begingroup\$ Does this answer your question? Different and opposing voltage sources? \$\endgroup\$
    – The Photon
    Commented Jan 13, 2022 at 19:59

2 Answers 2


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.


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