Kirchhoff's law

Gustav Robert Kirchhoff, a German physicist, was born on1824, in Konigsberg, Prussia. His first research topic was on the conduction of electricity. He developed a pair of laws that deal with the conservation of current and energy within electrical circuits. These two laws are commonly known as Frist Kirchhoff’s Voltage Law and the second Kirchhoff's Current Laws.

 Since these laws apply to all-electric circuits, understanding their fundamentals is paramount in understanding how an electronic circuit functions. Although these laws have immortalized Kirchhoff in the field of Electrical Engineering, he has additional discoveries. 

 1.He was the first person to verify that an electrical impulse traveled at the speed of light. Furthermore.

 2. Kirchhoff made a major contribution to the study of spectroscopy, and he advanced the research into blackbody radiation.

These laws help in calculating the electrical resistance of a complex network or impedance in the case of AC and the current flow in different streams of the network. We will discuss this in the next post.

1. Krichhoffis's Current law( KCL)

According to the law in any network of wires carrying currents, the algebraic sum of the all current meeting at a point ( or junction ) is zero. In other words, the sum of incoming currents towards any point is equal to the sum of outgoing currents from the point.

if I1,  I2, I3, I4, I5, and I6 are the currents meeting at junction 'O' flowing in the direction of the arrowheads marked on them. 

Note. 

We consider in-circuit incoming currents always as positive and outgoing currents negative, according to Kirchhoff's first low(KCL). 

       I1 - I2 -  I3+  I4 +  I15 -  I6 = 0      

 Or  I1  +  I4 +  I5 =  I2 +  I3 +   I6     

                                                                                                                                                                                                                                                                      Image .1

2. Kirchhoff's Voltage Law( KVL)

'The sum of all the voltages (rises and drops) around a closed loop is equal to zero.' In other words, the algebraic sum of all voltage rises is equal to the algebraic sum of all the voltage drops around a closed loop. 

We can solve the complex DC and AC network circuits with the help of the Kirchhoff law.

Example In each of the circuit diagrams in the given image, write the mesh equations using KVL.

Image.2

(Image) contains a single loop hence a single current, 'I' is flowing around it. Therefore a single equation will result as given below
Vs = IR1 + IR2