Kirchhoff’s Laws Kirchhoff’s Current Law (KCL) Kirchhoff’s Voltage Law (KVL) Kirchhoff’s Laws derivation

                              Kirchhoff’s Laws     

 

Kirchhoff’s Circuit Laws are two equalities that deal with the conservation of charge and energy in electrical circuits.

 

There basically two Kirchhoff’s Law :-

 

01. Kirchhoff’s Current Law (KCL) - Based on principle of conservation of electric charge.

 

02.  Kirchhoff’s Voltage Law (KVL) - Based on principle of conservation of energy.

 

               Kirchhoff’s Current Law (KCL)

       

⃝  The rule is also called Kirchhoff’s first law, Kirchhoff’s point rule, Kirchhoff’s junction rule (or nodal rule).

 

⃝   It states that at the junction, sum of current entering the junction is equal to the sum of current leaving the junction.

 

                              

 Junction is any point in the circuit.

 

⃝  Consider a case where I1 and I2 are the current entering the junction and,current I3, I4 and I5 are exiting out of the junction.

 

According to Kirchhoff’s law; I1 + I2 =I3 + I4 + I5 

                                  ∑ I = 0

 

 

       Kirchhoff’s Voltage Law (KVL)

 

⃝  The law is also called Kirchhoff’s second law, Kirchhoff’s loop rule.

 

 

⃝   It states that in a closed loop,algebraic sum of Emf is equal to the algebraic sum of product of resistances and respective currents flowing through them.

 

⃝   Consider a simple circuit having Emf = E1 and E2; R1 and R2 =resistances; current =I1 and I2.

 

Then according to this law : E1+E2= I1R1+ I2R2

                                           

 

⃝   For example:- 

 

                  

 

⃝   Consider given figure,let Emfs be E1 and E2 internal resistances be R1, R2 and R3.

⃝    Steps to use Kirchhoff’s law:-

 

Choose the loop to apply Kirchhoff’s law.

:-  Assume any direction.

 

:-   Emf is positive if assumed direction leaving positive terminal of battery.

 

:-   IR is positive if the current in the assumed direction.

 

:-   Consider closed loop ABCDFA, using the assumptions;

 

:-   E2=+R2I3 +R3I2 ;where I3=current flowing through R3

 

:-   Closed loop FCDEF,    +E1= +I1R1 + I3R2

 

:-   Closed loop ABDEA,   -E1 + E2 = -I1R1 +I2R3

 

:-   If the direction of current is taken opposite then

 

:-   Closed loop ABCDFA ;   -E2=-R2I3-R3I2

 

:-   FCDEF;    -E1= -I1R1 - I3R2

 

:-   ABDEA;    +E1 - E2 = +I1R1 -I2R3