**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 an electrical circuit loop, in an electrical circuit.

**Kirchhoff’s Current Law (KCL)**

#### This is Kirchhoff’s first law.

#### The sum of all currents that enter an electrical circuit junction is 0. The currents enter the junction have the positive sign and the currents that leave the junction have a negative sign:

#### 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**

*I*_{1} and *I*_{2} enter the junction

*I*_{3} leave the junction

*I*_{1}=2A, *I*_{2}=3A, *I*_{3}=-1A, *I*_{4}= ?

**Solution:**

#### ∑*I*_{k} = *I*_{1}*+I*_{2}*+I*_{3}*+I*_{4 }= 0

_{k}

*I*_{4}* = -I*_{1}* – I*_{2}* – I*_{3 }= -2A – 3A – (-1A) = -4A

#### Since *I*_{4} 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 example

*V*_{S} = 12V, *V*_{R1} = -4V, *V*_{R2} = -3V

_{S}

*V*_{R3} = ?

**Solution:**

#### ∑*V*_{k} = *V*_{S }+* V*_{R1 }+* V*_{R2 }+* V*_{R3 }= 0

_{k}

_{S }

*V*_{R3} =* *–*V*_{S }–* V*_{R1}* *–* V*_{R2} = -12V+4V+3V = -5V

_{S }