KIRCHHOFF'S LAWS

 Introduction:

                A German physicist Gustav Kirchhoff developed two laws enabling easy analysis of interconnection of any number of circuit elements. The first law deals with the flow of current and is popularly known as Kirchhoff’s Current Law (KCL) while the second one deals with the voltage drop in a closed network and is known as Kirchhoff’s Voltage Law (KVL).

Kirchhoff’s Current Law:

Statement:

                The algebraic sum of the currents meeting at a junction in an electrical circuit is zero.

Σ I = 0


As per the Kirchhoff’s Current Law,

i1 + i2 – i3 – i4 – i5 + i6 = 0 -----------(1)

                The direction of incoming currents to a junction is taken as positive while the outgoing currents are taken as negative.

The equation (1) can also be written as:

i1 + i2 + i6 = i3 + i4 + i5

i.e., Sum of incoming currents = Sum of outgoing currents 

Hence, Kirchhoff’s current law may also be stated as under,

                 The sum of currents flowing towards any junction in an electrical circuit is equal to the sum of  currents flowing away from that junction. 

                 Kirchhoff’s current law is also called junction rule. 


Kirchhoff’s Voltage Law:

Statement:

                In any closed electrical circuit, the algebraic sum of all the electromotive forces (e.m.fs) and voltage drops in resistors is equal to zero. 

i.e., In any closed circuit or mesh, 

Algebraic sum of e.m.fs + Algebraic sum of voltage drops = 0

Σ E + Σ V = 0

Kirchhoff’s voltage law is also called loop rule. 

Let us verify this statement with the help of the following example.

                The above circuit diagram consists of a voltage source, VS in series with two resistors R1 and R2. The voltage drops across the resistors R1 and R2 are V1 and V2 respectively.

Apply KVL around the loop,

VS−IR1−IR2=0

VS= IR1+IR2

⇒VS=V1+V2

                In the above equation, the left-hand side term represents single voltage source VS. Whereas, the right-hand side represents the sum of voltage drops. In this example, we considered only one voltage source. That’s why the left-hand side contains only one term. If we consider multiple voltage sources, then the left side contains sum of voltage sources.



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