Kirchhoff's Circuit Law | KCL | KVL

 Kirchhoff's Law

Kirchhoff's Circuit law are two types that deals with current and Potential (Voltage) difference in the electrical circuits.

1. Kirchhoff's Voltage Law (KVL):

                                                        Kirchhoff's Voltage law states that "the algebraic sum of  all branch voltages around any closed loop of the network is always zero at all instant of time. i.e.

                                               V+V1+V2+V3 = 0

All element's voltage act in Opposite direction of the voltage source.

KVL is the consequence of law of conservation of energy. Voltage said to be as Energy per unit charge.

So, if  Voltage or Energy source is increases then drop voltage of each elements will rise which is called Voltage Rise. Similarly if decreases then Drop voltage will also decreases.

we may define Kirchhoff's voltage Law, Around any closed loop at any instant of time the sum of the Rise voltage must be equal to the sum of the Drop Voltages in the Circuit.

In above Figure,

Clockwise Loop direction selected for the application of KVL. Starting at Node A assigned the positive sign to the voltage and Drop voltage polarity from + to - for the opposite order.

Simply have to understand that Voltage goes from source passed through the element then the first side of that element will assume that as +ve sign.

2. Kirchhoff's Current Law:

Kirchhoff's Current Law (KCL) states that "At a Node, the algebraic sum of the branch current is always zero at all instant of the time."

In other words,

                      At a Node, total incoming current is always equal to total leaving current. Algebraic sum of total currents at a Node is Zero.

KCL is a consequence of Law of conservation of Charge.

The Sum of Currents entering a node must be equal to the sum of currents leaving the Node.

 

By KCL at Node O,

incoming current at Node O = I1 and I2

Leaving current at Node O   =  I3 and I4

So,

I1+I2+I3+I4=0.

Mathematical Expression for KVL and KCL:

Reference Direction of Voltage and Current for any Passive element & V-I Relationship for Passive Elements: