Unit 2.1 - Kirchoff

# Unit 2.1 - Kirchoff - EE302: 2.1 - Physical Basics Gustav...

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9/13/10 Dr. Bruce McCann 1 EE302: 2.1 - Physical Basics Kirchhoff’s Current Law 2 Gustav Robert Kirchhoff Gustav Robert Kirchhoff (1824-87) was a Prussian physicist who published his circuit laws in 1845 while still a student. He also established the correct relationship between current and electrostatics. He later made fundamental contributions to the study of black body radiation and spectral analysis of solar radiation. 3 Kirchhoff’s Current Law (KCL) An informal statement of KCL: All of the current that enters a node must leave the node instantaneously. • A node cannot store charge. • A node cannot create or destroy charge. Hydraulic Analogy All of the fluid entering a tee must leave. What else could it do? KCL is a statement of Conservation of Mass. 4 Calculating Currents A ball enters the “T” at the left end… What can happen to it? It could come out here… or here… There are no other options!! 5 Calculating Currents Con’t What if I send a total of 10 C of charge… 10 C 6 Calculating Currents Con’t 10 C How much charge Comes out each path? 3 C 7 C 2 C 8 C 5.7 C 4.3 C

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9/13/10 Dr. Bruce McCann 2 EE302: 2.1 - Physical Basics 7 Calculating Currents Con’t We don’t deal with charge. We deal with current… 10 C I left I down I right Since charge has to be “conserved” so does current!!! 8 Kirchhof’s Current Law (KCL) Important Point: It is important to define our direction of positive current before using KCL The sum of current entering a “T” (node) in an electrical circuit MUST EQUAL the current leaving the “T” 9 Kirchhoff’s Current Law (KCL) KCL: The algebraic sum of the currents entering any node is zero. Equivalent statements: The algebraic sum of the currents leaving any node is zero. The sum of the currents entering any node is equal to the sum of currents leaving. 10 Kirchhoff’s Current Law I 1 I 2 I 5 I 4 I 3 Currents are signed quantities. Let’s treat currents flowing into a node as positive and currents flowing out of a node as negative . 11 Kirchhoff’s Current Law (KCL) I 1 I 2 I 5 I 4 I 3 I 1 I 2 I 3 I 4 + I 5 = 0 The algebraic sum of the currents leaving any node is zero. 12 Kirchhoff’s Current Law (KCL) 3 5 + I 3 − − 8 ( ) + 2 ( ) = 0 I 1 =3A I 2 =5A I 5 =-2A I 4 =-8A I 3 =? The algebraic sum of the currents leaving any node is zero.
9/13/10 Dr. Bruce McCann 3 EE302: 2.1 - Physical Basics 13 KCL….One More Time… 3 5 I 3 − − 8 ( ) + 2 ( ) = 0 I 5 =-2A I 4 = 8A I 1 =3A I 2 =5A I 3 =? The algebraic sum of the currents leaving any node is zero. I 5 = 2A I 4 =-8A 3 5 I 3 + 8 2 = 0 I 1 =3A I 2 =5A I 3 =? Reverse I

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## This note was uploaded on 11/01/2010 for the course EE 302 taught by Professor Mccann during the Fall '06 term at University of Texas at Austin.

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Unit 2.1 - Kirchoff - EE302: 2.1 - Physical Basics Gustav...

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