On what principle Kirchhoff’s current law is based?

Hint: Kirchhoff’s laws of electrical networks consist of two laws. The current law and the voltage law. These laws are based on basic conservation laws of physics. The Wheatstone bridge is a beautiful application of Kirchhoff’s laws.

Complete step by step solution:
We know that Kirchhoff proposed two laws for electrical networks. The first law or the Kirchhoff’s current law and the second law or Kirchhoff's voltage law. Regarding the question we will only start with the current law.
The statement of the current law is: Algebraic sum of all current meetings at any junction of an electrical network is always equal to zero.
That is, $\sum {I = 0} $
This law is also known as Kirchhoff’s junction rule.
This law is based on a certain sign convention that at a junction incoming current is positive and outgoing current is negative.
If at a junction O, there are three incoming currents ${I_1},{I_2}\& {I_3}$ and two outgoing currents ${I_4}\& {I_5}$
Then for the electrical network or junction, according to Kirchhoff’s law,
$\sum {I = 0} $
$ \Rightarrow {I_1} + {I_2} + {I_3} - {I_4} - {I_5} = 0$ (due to sign convention, outgoing currents are assigned negative sign)
$ \Rightarrow {I_1} + {I_2} + {I_3} = {I_4} + {I_5}$

This means that at an electrical junction, total incoming current must be equal to total outgoing current. As we can see here, there is no current being accumulated at any junction. So we can say that Kirchhoff’s current law or junction rule is based on the law of conservation of electric charge.

Note: The examiner can also ask us otherwise, which law is based on the law of conservation of electric charge. And also keep in mi9nd that Kirchhoff’s voltage law or loop rule is based on the law of conservation of energy, that is, total energy in an electrical loop is always conserved.