Validity of Kirchhoff's current law Is Kirchhoff's current law valid for rapidly varying currents such as a one with a frequency in the order of 10KHz?
 A: It's all about time constants. Kirchhoff's Laws assume that the steady state has been achieved. 
How do you know if you can make that assumptions in the presence of of time varying driving signals? By comparing the time scale of the external variation with the time-scale of transients in the circuit.
There are two cases to check first


*

*Capacitance and inductance driven time-scale For a basic RC series circuit (that is one with a resistance $R$ and a capacitance $C$ in series) the time constant is $\tau = RC$ (you should check for yourself that this has units of time, BTW), and if 
$\tau \, f \ll 1 $
where $f$ is the frequency of the driving signal, then you can reasonably use Kirchhoff's Laws for this case.

*Physical extent time-scale Generally if the circuit is much smaller than $c/f$ than you can ignore the transmission delay around the circuit, but if this is not true you have to worry about propagation delays. People who work on very high frequency circuits have lots of rules of thumb that contradict the ones that are used with ordinary, slowly varying circuits like the one you build on a bench in a first year lab course.
