Violation of KVL ,KCL at high Frequencies question:
How can we prove mathematically that KVL (Kirchoff's volatage law) and KCL (Kirchoff current law) become invalid at very large frequencies?
i have read this statement in my book but it doesn't explain the fact that why KVL , KCL fails at High frequency 
is that because condcuting wires in very circuit , at high frequency start to pose reactances,  and don't act like lumped elements(whose electrical length is very less than operating wavelength) 

can anyone explain me more at atomic level that what happens inside any resistive Electric circuit(of course condcuting wires are also present) driven by source when source's freqency increases indefinitely 

 A: 
KCL and KVL both depend on the lumped element model being applicable to the circuit in question. When the model is not applicable, the laws do not apply. KCL and KVL result from the assumptions of the lumped element model.
KCL is dependent on the assumption that the net charge in any wire, junction or lumped component is constant. Whenever the electric field between parts of the circuit is non-negligible, such as when two wires are capacitively coupled, this may not be the case. This occurs in high-frequency AC circuits, where the lumped element model is no longer applicable. For example, in a transmission line, the charge density in the conductor will constantly be oscillating.

Source : https://en.m.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws
A: At high frequencies circuits behave like transmission lines, meaning that electromagnetic waves will propagate along the circuit. Unlike "regular voltages" and currents these waves possess a dependence of the their amplitude dependening on the distance they have travelled. This means, that the kirchhoff laws do not apply anymore Generally, there will be a superposition of a forward and backward going (voltage/current) wave. These waves are usually proportional to a factor of $$e^{+/- ikx}$$, with $$k=2 \pi/\lambda$$ denoting the wave vector of the wave,$$\lambda$$ its wavelength, $$i$$ denoting the imaginary unit and $$x$$ denoting the distance  of the waves to the generator. For low frequencies, the term $$e^{+/-ikx}$$ will be small because the the wavelength will be small. Thus, $$e^{i*0}=1$$ and the the propagating waves are nearly constant with distance and only dependent on the time. This should be the limit, when wave effects can be neglected. To my knowledge (dont take this for granted) for practical purposes wave effects have to be considered when the dimension of the transmission line/or circuit exceeds a length of $$\lambda/10$$.
For example unintuitively power transmission lines that work on very low frequencies are also modelled in the same manner as high frequency.transmission lines for radio waves, because the cover huge distances. For more on tranmission lines you can get started here:https://en.wikipedia.org/wiki/Transmission_line
A: Kirchhoff's voltage law (KVL) in its modern form is always valid, due to definition of voltage: difference of potentials. Since potential is a function of position, sum of voltage drops along a closed loop is always zero. This has nothing to do with the Faraday law, which concerns total electric field: the voltage drops across any path segment do not, in general, reflect total electric field there, but only its potential part.
Kirchhoff's current law (KCL) ceases to be valid when the electric current charging up wire surfaces ceases to be negligible when compared to current flowing along the wires. This happens when electric current in the circuit oscillates with very high frequency.
