Kirchhoff's Laws
Kirchhoff's current law and voltage law, defined by Gustav Kirchhoff, describe the relation of values of currents that flow through a junction point and voltages in a an electrical circuit loop, in an electrical circuit.

Kirchhoff's current law (KCL)

Kirchhoff's voltage law (KVL)

Kirchhoff's Current Law (KCL)
This is Kirchhoff's first law. The sum of all currents that enter an electrical circuit junction is 0. When the currents enter the junction have positive sign and the current that leave the junction have negative sign:
KCL

Another way to look at this law is that the sum of currents that enter a junction is equal to the sum of currents that leave the junction:

KCL example
I₁ and I₂ enter the junction I₃ leave the junction
I₁ =2A, I₂ =3A, I₃ =-1A, I₄ = ?

Solution:
∑I_k = I₁ +I₂ +I₃ +I₄ = 0
I₄ = -I₁ - I₂ - I₃ = -2A - 3A - (-1A) = -4A
Since I₄ is negative, it leaves the junction.

Kirchhoff's Voltage Law (KVL)
This is Kirchhoff's second law. The sum of all voltages or potential differences in an electrical circuit loop is 0
KVL

KVL example
V_S = 12V, V_R1 = -4V, V_R2 = -3V V_R3 = ?

Solution:
∑V_k = V_S + V_R1 + V_R2 + V_R3 = 0
V_R3 = -V_S - V_R1 - V_R2 = -12V+4V+3V = -5V
The voltage sign (+/-) is the direction of the potential difference.

See also