State and explain Kirchhoff's first law (Junction law) and Kirchhoff's second law (Loop rule).

(N/A) Kirchhoff's First Law (Junction Law):
Statement: At any junction,the sum of the currents entering the junction is equal to the sum of the currents leaving the junction.
Mathematically,the algebraic sum of currents at any junction is zero: $\sum I = 0$.
This law is based on the principle of conservation of charge.
Kirchhoff's Second Law (Loop Rule):
Statement: The algebraic sum of changes in potential around any closed loop involving resistors and cells is zero.
Alternatively,for any closed loop,the algebraic sum of the products of resistances and their respective currents is equal to the algebraic sum of the electromotive forces (EMFs) applied along the loop: $\sum IR = \sum \varepsilon$.
This law is based on the principle of conservation of energy.
Sign Conventions:
$1$. When moving in the direction of current,the potential drop across a resistor is taken as negative $(-IR)$.
$2$. When moving against the direction of current,the potential change is taken as positive $(+IR)$.
$3$. When moving from the negative to the positive terminal of a battery,the $EMF$ is taken as positive $(+\varepsilon)$.
$4$. When moving from the positive to the negative terminal of a battery,the $EMF$ is taken as negative $(-\varepsilon)$.