# What is Kirchhoff's voltage law all about?

what is the Kirchhoff voltage law ? isnt it the sum of potential drops as we move along a circuit till the same point should be zero

it is simply energy conservation law that when the battery creates certain potential difference then while going through then while going to the circuit the circuit that potential energy should be used up ?

my question is about short circuiting when we short circuit a wire then Kirchhoff's voltage law is violated .. but how ?

as we short circuit a wire the potential energy of electrons gets converted to kinetic energy as in a superconducting wire where there is no resistance the electrons are pushed by the negative end and attracted by the positive end so from positive terminal to negative terminal in the battery a field acts on them and they accelerate and when they reach the positive terminal the entire energy due to potential difference is converted into kinetic energy ... so why we say that Kirchhoff's laws are violated here ??

the potential difference has been used up as kinetic energy

• What are the poor communication skills of today's youth all about? – Samuel Oct 26 '13 at 11:01
• @Samuel I don't know, I am constantly editing questions on this site to fix blatant disregards for punctuation, capitalization, and grammar. I'm fine with some grammar issues stemming from non-native English speakers, but it's ridiculous at times. – JYelton Oct 27 '13 at 0:52

Connecting a wire across a battery's terminals does not violate Kirchhoff's voltage law. You have assumed that a battery is an ideal voltage source, but it is not. You have assumed that a common physical wire is an ideal wire, but it is not.

An ideal voltage source can deliver infinite current at the specified voltage, and a real battery clearly cannot do this. The current delivered by a real battery is limited by the chemical reactions taking place and by the internal resistance of the battery. An ideal wire has no resistance, no inductance, and no capacitance. A real wire has all of these, and they limit the behavior of the physical wire.

Kirchhoff's laws hold as long as your circuit does not involve subatomic reactions, such as the radioactive decay of some substance. If you think you have found a violation then you have not modeled your circuit correctly.

... then Kirchhoff's voltage law is violated .. but how ?

KVL is exact as long as the electric fields are conservative (the closed line integral of conservative electric field is zero) and only approximate when there are time varying currents and, thus, time varying magnetic fields, present.

So, as you soon as you start thinking about circuits that don't remotely approximate a circuit with steady current, such as the example you give, throw KVL out the window.

From Wikipedia:

KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop. This is not a safe assumption for AC circuits.[2] In the presence of a changing magnetic field the electric field is not a conservative vector field. Therefore the electric field can not be the gradient of any potential. That is to say, the line integral of the electric field around the loop is not zero, directly contradicting KVL.

Kirchoff's voltage and current laws are idealized models, that is: we use them to make sense of practical circuits in a schematized, lumped and idealized way. They are not laws of nature, i.e. violating Kirchoff's voltage and current laws does not mean you found some kind of new natural phenomenon. They are just a model with which it is possible to generate equations that help us design and simulate electrical circuits.

Many things make no logical sense in KVL and KCL, for instance the always interesting case of 'radiation'. When in some special cases (like a voltage source connected to a capacitor) the laws seem not to hold and energy seems to just 'disappear', we either say this is radiated away or we say that this kind of situation fundamentally transcends the scope of these simplified 'laws'.

Models model reality, not the other way around!

• How does connecting a capacitor across a voltage source violate either KCL or KVL? Both laws work perfectly in the case of ideal voltage sources and ideal capacitors. – Joe Hass Oct 26 '13 at 12:28
• @JoeHass, as I understand it, your comment is subtly incorrect. If (1) an uncharged ideal capacitor is connected to an ideal voltage source via, e.g., an ideal switch and (2) KVL holds, the current through the capacitor is undefined at the instant the switch is closed. If KVL holds, the voltage across the capacitor is $V_S\cdot u(t)$ and so, the derivative of the capacitor voltage doesn't exist at $t = 0$. But the capacitor current is proportional to the derivative of the capacitor voltage so the capacitor current doesn't exist at $t = 0$. (cont.) – Alfred Centauri Oct 26 '13 at 15:04
• @JoeHass (cont.) Now, you may argue that there is an impulse of current at $t=0$ but we're already on shaky ground here since we're out of the realm of ideal circuit theory altogether which assumes that the rates of change are small enough that electromagnetic effects can be ignored. This is similar to the "two capacitor missing energy paradox" that demonstrates what happens when we forget the assumptions underlying ideal circuit theory. – Alfred Centauri Oct 26 '13 at 15:07
• @AlfredCentauri Your point is well taken. On the other hand, the OP and user36129 did not add a switch to their circuits and didn't talk about a transient analysis. My point was that the presence of a capacitor across a voltage source does not inherently violate KCL or KVL and I was hoping to combat the misconception that a capacitor stores charge (i.e. that the current in one terminal is different than the current out of the other terminal). You are well respected here and I appreciate your comments. – Joe Hass Oct 26 '13 at 19:38