Kirchhoff’s Laws in AC Circuits

Kirchhoff’s laws for D.C. circuits are equally applicable to A.C. circuits, if the vector impedance Z replaces the resistance in the network and the emfs and currents are in complex form.
    We can add series impedances as
        Z = Z₁ + Z₂ + Z₃ + ….. Z_n.

Impedances in parallel (like resistances in parallel) add by reciprocals.
        1/Z = 1/Z₁ + 1/Z₂ +1/Z₃ + … 1/Z_n.
The reciprocal of the impedance is called the admittance Y. Thus for the combination of parallel impedances we can write
        Y = Y₁ + Y₂ + Y₃ + Y_n.

Kirchhoff’s laws are as follow:
(1)    As there is no accumulation of electric charge in a system of conductors, the sum of complex currents entering any junction equals the sum of the complex currents leaving that junction.
The algebraic sum of all the complex currents meeting at a common junction is zero.
        ∑I = 0.

(2)    The sum of the complex emf’s in any mesh equals the sum of the complex potential drops across all elements of that mesh.
∑E = ∑ZI.