Electrical Circuits & Network Theorems: Definition Of Kirchhoff's Current Law (KCL) And Kirchhoff's Voltage Law (KVL)

Definition Of Kirchhoff's Current Law (KCL) And Kirchhoff's Voltage Law (KVL)

Kirchhoff’s laws are also known as “fundamental circuit laws”, in which we studied about “Kirchhoff’s 1^st law and Kirchhoff’s 2^nd law”. In higher studies “Kirchhoff’s 1^st law and Kirchhoff’s 2^nd law” are well known as “Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL) respectively.”

KIRCHHOFF’S CURRENT LAW (KCL):-

According to this law, “Algebraic sum of total currents taking at a point/node/junction is equals to zero.”

i.e., ∑I_N=0

Where, N=0, 1, 2, 3, 4……..

Assumption to be considered:-

Let us consider a circuit,

We assume that, current entering at point/node/junction is taken as +ve and current leaving from same point/node/junction is taken as –ve.

From above figure, ‘i₁’, ‘i₂’, ‘i₃’ is taken as +ve and ‘i₄’, ‘i₅’, ‘i₆’ is taken as –ve.

Applying KCL at point ‘o’, we get

∑I_N=0

i₁+ i₂+ i₃+(-i₄)+(-i₅)+(- i₆)=0

i₁+ i₂+ i₃-i₄-i₅- i₆=0

i₁+ i₂+ i₃= i₄+i₅+ i₆

↓ ↓

(incoming current) (outgoing current)

From the above result, we can also redefine the KCL as, “Total incoming current at a point/node/junction is equals to the total outgoing current at same point/node/junction”.

KIRCHHOFF’S VOLTAGE LAW(KVL):-

According to this law, “The Algebraic sum of voltage drops in a closed path/loop is equals to zero”.

i.e., ∑V_N=0

Where, N=0, 1, 2, 3, 4……..

Closed loop means, ‘initial and final point are said to be same.’ like,

In other word, we can also define KVL as “In any closed loop, algebraic sum of total emf and the product of current and the resistance are taken as zero”.

i.e, E₁+E₂+E₃+…..+E_N+IR₁+IR₂+…..+IR_N=0

Where, N=0, 1, 2, 3, 4……..

Assumption to be considered:-

(1)In case of a resistance:-

(a) When we going from ‘A’ to ‘B’ and current ‘i’ also flows in same direction.

Then, voltage ‘v’ across the resistance is taken as –ve.

V= (-)I∙R

(b)When we going from ‘B’ to ‘A’ and current flows from ‘A’ to ‘B’. i.e., in opposite direction.

Then, voltage ‘v’ across the resistance is taken as +ve.

V= (+)I∙R

(2) In case of a voltage source:-

Through a voltage source, our direction is not considered. P.d across the voltage source only depends upon direction of current.