The Governing Equations of a Multi Loop Circuit
Transcript of The Governing Equations of a Multi Loop Circuit
logo1
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
logo1
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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∑ 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 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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u- -
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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 andout of a node is zero.
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u- -
HHHj
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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.
HHHHH
HHHHHH
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u- -
HHHj
���*
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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
HHHHHH
HHHHHHH�
������
������
��
u- -
HHHj
���*
���*
HHHj
∑ 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
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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
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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
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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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node
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E(t) = R1i1 +1C
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∫i3 dt
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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loop 1
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∫i3 dt = 0
Bernd Schroder Louisiana Tech University, College of Engineering and Science
The Governing Equations of a Multi Loop Circuit