# What are KCL and KVL

## Kirchhoff's laws

The Kirchhoff current and voltage law defined by Gustav Kirchhoff describes the relationship between the values โโof currents flowing through a connection point and the voltages in a circuit loop in a circuit.

### Kirchhoff's current law (KCL)

This is Kirchhoff's first law.

The sum of all currents entering a circuit junction is 0. The currents entering the junction have a positive sign and the currents leaving the junction have a negative sign:

Another way to look at this law is that the sum of the currents entering a transition is equal to the sum of the currents exiting the transition:

#### KCL example

*I. *_{1} and *I. *_{2} enter the intersection

*I. *_{3} leave the intersection

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

Solution:

โ *I. _{k}* =

*I.*

_{1 }

*+ I*

_{2 }

*+ I*

_{3 }

*+ I*

_{4}= 0

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

There *I. *_{4} is negative, it leaves the intersection.

### Kirchhoff's Voltage Law (KVL)

This is Kirchhoff's second law.

The sum of all voltages or potential differences in a current loop is 0.

#### KVL example

*V. _{S.}* = 12 V,

*V.*

_{R1}= -4 V,

*V.*

_{R2}= -3V

*V. *_{R3} =?

Solution:

โ *V. _{k}* =

*V.*+

_{S.}*V.*

_{R1}+

*V.*

_{R2}+

*V.*

_{R3}= 0

*V. *_{R3} = - *V. _{S.}* -

*V.*

_{R1}-

*V.*

_{R2}= -12

*V.*+ 4

*V.*+ 3

*V.*= -5 V.

The voltage sign (+/-) is the direction of the potential difference.

### See also

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