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The Laws An Example

The Governing Equations of a Multi LoopCircuit

Bernd Schroder

Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

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The Laws An Example

Kirchhoff’s Laws

1. Kirchhoff’s Voltage Law. The sum of the voltages in aclosed 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.

∑vloop = 0u

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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, wecould indefinitely accelerate a charge by sending it around.

∑vloop = 0u

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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.

∑vloop = 0u

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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.

∑vloop = 0u

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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 thevoltages on the elements is equal to the external voltage.

2. Kirchhoff’s Current Law. The sum of the currents into andout of a node is zero.

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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 andout of a node is zero.

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∑ iin = ∑ iout

Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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.

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∑ iin = ∑ iout

Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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

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∑ iin = ∑ iout

Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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, chargeswould either be created or destroyed at the node. (There isno storage in conductors.)

3. Council’s Law (honorable mention). Never become part ofthe circuit.

Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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 isno storage in conductors.)

3. Council’s Law (honorable mention). Never become part ofthe circuit.

Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

Kirchhoff’s Laws1. 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 isno storage in conductors.)

3. Council’s Law (honorable mention). Never become part ofthe circuit.

Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

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The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit

logo1

The Laws An Example

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Bernd Schroder Louisiana Tech University, College of Engineering and Science

The Governing Equations of a Multi Loop Circuit