Can any electrical circuit be solved i.e. analysed (potentials, currents, charges etc. found out) solely by Kirchhoff's circuit laws?

by Kirchhoff's circuit laws I mean,

1.Kirchhoff's current law : The algebraic sum of currents in a network of conductors meeting at a point is zero. Recalling that current is a signed (positive or negative) quantity reflecting direction towards or away from a node, $${ \sum _{k=1}^{n}{I}_{k}=0}$$


2.Kirchhoff's voltage law: The directed sum of the electrical potential differences (voltage) around any closed network is zero, $$\sum _{k=1}^{n}V_{k}=0$$

What I mean is that can I analyse a given circuit fully by applying Kirchhoff's circuit laws. Can there be any information I can not find by Kirchhoff's circuit laws (any information that is only findable by some other method). Please answer the question both theoretically and practically

  • $\begingroup$ Well, the answer is "yes". What else are you looking for? $\endgroup$
    – DanielSank
    Dec 28, 2016 at 16:03
  • 1
    $\begingroup$ There's plenty of them, because there's more variables in the real world than there is in the circuit model. For example, you can't use Kirchoff's laws to determine the most likely location of a given electron. In order to answer this with yes or no, we would need a comprehensive list of exactly what class of circuits you are analyzing and exactly what properties you are interested in. That being said, in my school career, I never once came across a circuit that could not be sufficiently analyzed by these methods. $\endgroup$
    – Cort Ammon
    Dec 28, 2016 at 16:11
  • $\begingroup$ @DanielSank, you should reconsider. See my answer. $\endgroup$
    – The Photon
    Dec 28, 2016 at 16:51
  • $\begingroup$ @ThePhoton oh, right, the constitutive relations are important too. Duh. $\endgroup$
    – DanielSank
    Dec 28, 2016 at 17:20

2 Answers 2



Kirchhoff's laws give relations that stem from the topology of the circuit --- how the components are connected. But they don't take any account of what kind of components are making those connections.

So you also need to have some information about the behavior of the elements. For example, an ideal resistor passes a current proportional to the voltage applied to it (a relationship called Ohm's Law). Or that an ideal voltage source provides a fixed voltage, allowing any amount of current to pass through it. As DanielSank reminded me, the equations describing the individual circuit elements are called constitutive relations.

With either KCL or KVL and the equations describing the components making up the branches of the circuit, you can solve any realistic circuit. This is called mesh analysis when done with KVL, or nodal analysis when using KCL.

It's also possible to draw a nonsense circuit that can't be solved by any method at all --- for example with two different-value voltage sources connected in parallel. These "circuits" are simply logical contradictions, not modeling any real physical circuit, so there's no loss by not being able to solve them.

Another limitation, KCL and KVL apply only to lumped circuits. That is, circuits whose physical dimensions are much smaller than the wavelengths associated with the highest frequency signal present in the circuit. In large circuits you might see effects like radiation or transmission line delay that are not modeled by straightforward application of Kirchhoff's laws, although it is in many cases possible to produce an adequate equivalent lumped element model for distributed circuit elements to allow Kirchhoff's laws to be applied to the rest of the circuit they're connected to.

I should also add, that while linear circuits (composed of voltage sources, current sources, linear resistors, and linear controlled sources) can be solved by straightforward application of linear algebra to the KVL/KCL equations and the constitutive relations, it's possible to construct nonlinear circuits that are extremely difficult to solve, and for any particular numerical solution technique there's likely to be some circuit for which it fails.


No. Imagine a circuit composed of 4 equal resistances, $R$, connected in a square shape, one resistor per side, with enough conducting wire to make a (pick-a-number, say, 3 or 4) cm per side square. Then produce a spatially-uniform magnetic field perpendicular to the square and increasing in time (or varying with some other time function).

By Faraday's Law of induction (an application of Maxwell's Equations), there will be an induced electric field $\vec{E}$ resulting in a current $I$ in the loop and each resistor will have a voltage drop $IR$. The sum of the voltage drops is not zero. Kirchhoff's Voltage Law does not hold true in this situation.

This is just a simple example of what are known as non-potential voltages. Induction produces many real-world deviations from Kirchhoff's circuit laws, so designers and analyzers need to be careful.

If a real circuit isn't behaving like Kirchhoff's circuit laws predict, be sure that there isn't something inducing an emf and producing a stray current.

Also, Kirchhoff's laws do not tell you relationships of voltage, current and charge for ohmic devices, diodes, capacitors, inductors, transistors, or transformers.


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