Kirchhoff's law is electric networks in which steady currents are flowing. Kirchhoff's law is used to find the values of current, voltage, and internal resistance in DC circuits. we can find applying Kirchhoff's low the unknown resistance in the circuit. Wheatstone bridge is an important application of Kirchhoff's law. The first law states that the algebraic sum of the currents in all the conductors that meet at a point is zero. The second law states that the algebraic sum of the products of current and resistance in each part of any closed path in a network is equal to the algebraic sum of the electromotive forces in the path.


There are two formulas-

            1. Kirchhoff's Current Law
            2. Kirchhoff's Voltage Law

Kirchhoff's Current Law


The algebraic sum of the currents at any node or junction in an electrical network is zero.
That is,     
                Incoming Current = Outgoing Current

 


                 I1  + I3 = I2 + I4  + I5


       Or,     I1 – I2  + I3 – I4 – I5 ­= 0



Kirchhoff's Voltage Law

The algebraic sum of source EMF and drop voltage is zero.



So apply KVL in abgha mesh-

    Vab  +  Vbg  +Vgh  + Vha  =  0                                          

   Or, - I1R1 –I1R1 +  Vs2 – I1R3 +Vs1 = 0

 Or,   I1 (R1 +R2) +I2R2 –Vs1 –Vs2 = 0 


Problem-1: Determine the Current of the 12ohm Resistor-


Solution

Step -1

Detach the 12ohm resistor and take the value from terminal b and d


Therefore Voltage in terminal b,

Vb = 108 – 4I1

               = 108- 4 x 6

At d terminal,

Vd = 108 -8I2

               = 108 – 8x9

               = 36 V

So, Thevenin Voltage at terminals b and d

          VTh = Vb – Vd

                 = 84 – 36

                 =48 V

Or,


Step-2

Shorting the Voltage Source



Step-3

The Current flowing through 12-ohm Resistor is,

            = 2.7 A





 Example 2: Find out  V3 from the circuit.





Solution:

Applying KVL in loop ABCDA

+V3 -10 + 20 -50 +30 = 0
  Vs = 10V 
                    (Answer)


Application of Kirchhoff's


1. Kirchhoff's law is used in  analyzing series circuits

2. Kirchhoff's law is used in DC circuits or AC circuits  

3. Kirchhoff's law is used in complex circuits for problem-solving