When does a circuit, containing only independent voltage and current sources, violate Kirchoff's law?

Question

How do I know if the circuit below violates Kirchoff's law or not?

Answer 1

This is the kind of exercise designed to make you think about what Kirchhoff's Laws means.

If you think that these laws are just equations where you plug-in values, then yes, you can create a circuit where the laws are violated.

Here is one very simple. Pick an ideal DC voltage source and short-circuit it. No resistance, means that you end up with only one solution V=0. However, you can short-circuit a 12 V battery. What happens then?

The simplest answer is that your circuit is not not feasible. It does not exist. In the real world, we would have the resistance of the cable used to short-circuit the battery. As such, we would end up with Ohm's law: 12V = R.I. Based on the resistance, we can calculate the current.

Answer 2

A voltage source is something whose potential difference is fixed, cannot change, but whose current can be any value.

Therefore, any closed path around a circuit which contains only voltage sources is problematic, with individual sources vying to impose different potentials upon the same node. I won't say that such an arrangement necessarily "violates KVL", because it's possible that all the source are 0V, or they all do actually add up to zero around the loop. All these are bad:

^{simulate this circuit – Schematic created using CircuitLab}

If you find any such loop in your circuit, consisting exclusively of voltage sources, it's a potential violation (pun absolutely intended), not of any law, but rather of feasibility.

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A current source can have any potential difference, but the current through it is fixed. Since the potential difference is flexible, "loops" of current sources are not necessarily problematic, and we focus on nodes where current branches, which concerns KCL.

Any junction in the circuit, where all branches contain a current source, is problematic, including a two-path junction (sources in series). In such a node, it is possible that all source are 0A, or their values do indeed total zero, which would not violate KCL, but generally these are bad:

^{simulate this circuit}

If you can find any node in the circuit whose branches all contain a current source, you have found a "violation", even if the branch contains other components in series with the source.

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I understand why others here dislike the question's claim of some "violation of Kirchhoff's laws", I do too. Can you violate a "law"? Can you have two rods of 10cm length, end to end in a straight line and have the total length be anything other than 20cm?

If you add up all the voltages in a closed loop, and arrive at anything other than 0V, this isn't so much a violation of KVL as it is a situation which cannot exist in reality.

However, I think we all understand what you mean when you, or the professor, or the book says "violation of KVL or KCL", in the context of a hypothetical. I'm OK with that, as long as we all agree it can't happen in reality. At least, not in this one, and if our models are correct.

Answer 3

It's b because there is a loop of only voltage sources

In general solve the circuit determining an expression for the voltage at each node and the current through each edge, if the circuit cannot be solved it violates kirchoffs laws.

In the case of circuit B the current in the edges marked in red cannot be determined.

the easiest solving method for this analysis is probably superposition.