The Governing Equations of a Multi Loop Circuit
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The Laws An Example The Governing Equations of a Multi Loop Circuit Bernd Schröder Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. u C C C CC CC CC CC X X X X X X X X O X X X C C C CC CC CC CC Bernd Schröder The Governing Equations of a Multi Loop Circuit ∑ vloop = 0 logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. 1.2 Careful with signs. Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. 1.2 Careful with signs. 1.3 In loops with a source, we can also say that the sum of the voltages on the elements is equal to the external voltage. Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. 1.2 Careful with signs. 1.3 In loops with a source, we can also say that the sum of the voltages on the elements is equal to the external voltage. 2. Kirchhoff’s Current Law. The sum of the currents into and out of a node is zero. Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. 1.2 Careful with signs. 1.3 In loops with a source, we can also say that the sum of the voltages on the elements is equal to the external voltage. 2. Kirchhoff’s Current Law. The sum of the currents into and out of a node is zero. HH j H HH H * HH u HH H H H H jH H * HH H Bernd Schröder The Governing Equations of a Multi Loop Circuit ∑ iin = ∑ iout logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. 1.2 Careful with signs. 1.3 In loops with a source, we can also say that the sum of the voltages on the elements is equal to the external voltage. 2. Kirchhoff’s Current Law. The sum of the currents into and out of a node is zero. Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. 1.2 Careful with signs. 1.3 In loops with a source, we can also say that the sum of the voltages on the elements is equal to the external voltage. 2. Kirchhoff’s Current Law. The sum of the currents into and out of a node is zero. 2.1 It’s conservation of mass. If the sum was not zero, charges would either be created or destroyed at the node. (There is no storage in conductors.) Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example Kirchhoff’s Laws 1. Kirchhoff’s Voltage Law. The sum of the voltages in a closed loop is zero. 1.1 It’s conservation of energy. If the sum was not zero, we could indefinitely accelerate a charge by sending it around. 1.2 Careful with signs. 1.3 In loops with a source, we can also say that the sum of the voltages on the elements is equal to the external voltage. 2. Kirchhoff’s Current Law. The sum of the currents into and out of a node is zero. 2.1 It’s conservation of mass. If the sum was not zero, charges would either be created or destroyed at the node. (There is no storage in conductors.) 3. Council’s Law (honorable mention). Never become part of the circuit. Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 s B B B B B B B B B B PP PP R2 PP PP E(t) C qs Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 s node B B B B B B B B B B PP PP R2 PP PP E(t) C qs Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? PP PP R2 PP PP E(t) C qs Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? PP PP R2 PP PP E(t) C qs Bernd Schröder The Governing Equations of a Multi Loop Circuit i1 = i2 + i3 logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? PP PP R2 PP PP U E(t) loop 1 C qs Bernd Schröder The Governing Equations of a Multi Loop Circuit i1 = i2 + i3 logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? PP PP R2 PP PP U E(t) loop 1 C qs i1 = i2 + i3 E(t) = Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? PP PP R2 PP PP U E(t) loop 1 C qs i1 = i2 + i3 E(t) = R1 i1 Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? PP PP R2 PP PP U E(t) loop 1 C qs i1 = i2 + i3 1 E(t) = R1 i1 + C Bernd Schröder The Governing Equations of a Multi Loop Circuit Z i3 dt logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? U E(t) loop 1 U loop 2 R2 C qs PP PP PP PP i1 = i2 + i3 1 E(t) = R1 i1 + C Bernd Schröder The Governing Equations of a Multi Loop Circuit Z i3 dt logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? U E(t) loop 1 U loop 2 R2 C qs PP PP PP PP i1 = i2 + i3 1 E(t) = R1 i1 + C R2 i2 Bernd Schröder The Governing Equations of a Multi Loop Circuit Z i3 dt logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? U E(t) loop 1 U loop 2 R2 C qs PP PP PP PP i1 = i2 + i3 1 E(t) = R1 i1 + C Z 1 i3 dt R2 i2 − C Bernd Schröder The Governing Equations of a Multi Loop Circuit Z i3 dt logo1 Louisiana Tech University, College of Engineering and Science The Laws An Example R1 i1 i2 B B B B B - sB B B B B node i3 ? U E(t) loop 1 U loop 2 R2 C qs PP PP PP PP i1 = i2 + i3 1 E(t) = R1 i1 + i3 dt C Z 1 i3 dt = 0 R2 i2 − C Z Bernd Schröder The Governing Equations of a Multi Loop Circuit logo1 Louisiana Tech University, College of Engineering and Science
