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The Laws An Example The Governing Equations of a Multi Loop Circuit Bernd Schr oder logo1 Bernd Schr oder Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit The Laws An

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SLIDE 1

logo1 The Laws An Example

The Governing Equations of a Multi Loop Circuit

Bernd Schr¨

  • der

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 2

logo1 The Laws An Example

Kirchhoff’s Laws

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 3

logo1 The Laws An Example

Kirchhoff’s Laws

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

closed loop is zero.

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 4

logo1 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 Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 5

logo1 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.

∑vloop = 0

✉ ❈ ❈ ❈✄ ✄ ✄❈ ❈ ❈ ❈ ❈ ❈ ✄ ✄ ✄ ✄ ✄ ✄❈ ❈ ✄ ✄ ❈ ❈ ❈✄ ✄ ✄❈ ❈ ❈ ❈ ❈ ❈ ✄ ✄ ✄ ✄ ✄ ✄❈ ❈ ✄ ✄ ✘ ✘ ✘ ❳❳ ❳ ✘ ✘ ✘ ✘ ✘ ✘ ❳❳ ❳ ❳❳ ❳ ✘ ✘ ❳ ❳ ✛✘ ✙ ❖

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 6

logo1 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 Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 7

logo1 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 Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 8

logo1 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 Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 9

logo1 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
  • ut of a node is zero.

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 10

logo1 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
  • ut of a node is zero.

❍❍❍❍❍❍❍❍❍❍❍❍❍❍ ❍ ✟✟✟✟✟✟✟✟✟✟✟✟✟✟ ✟ ✉ ✲ ✲ ❍❍ ❍ ❥ ✟✟ ✟ ✯ ✟✟ ✟ ✯ ❍❍ ❍ ❥

∑iin = ∑iout

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 11

logo1 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
  • ut of a node is zero.

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

slide-12
SLIDE 12

logo1 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
  • ut 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 Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 13

logo1 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
  • ut 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 Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 14

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 15

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 node

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 16

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 node

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 17

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 node

i1 = i2 +i3

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 18

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 ❯ loop 1 node

i1 = i2 +i3

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 19

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 ❯ loop 1 node

i1 = i2 +i3 E(t) =

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 20

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 ❯ loop 1 node

i1 = i2 +i3 E(t) = R1i1

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 21

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 ❯ loop 1 node

i1 = i2 +i3 E(t) = R1i1 + 1 C

  • i3 dt

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 22

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 ❯ ❯ loop 2 loop 1 node

i1 = i2 +i3 E(t) = R1i1 + 1 C

  • i3 dt

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 23

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 ❯ ❯ loop 2 loop 1 node

i1 = i2 +i3 E(t) = R1i1 + 1 C

  • i3 dt

R2i2

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

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SLIDE 24

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 ❯ ❯ loop 2 loop 1 node

i1 = i2 +i3 E(t) = R1i1 + 1 C

  • i3 dt

R2i2 − 1 C

  • i3 dt

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit

slide-25
SLIDE 25

logo1 The Laws An Example

✚✙ ✛✘ ❇❇✂✂❇❇ ❇❇ ❇❇ ❇❇ ✂✂ ✂✂ ✂✂ R1 C ✲ ✲ ❄ i1 i2 i3 E(t) q s s ✏ ✏ P P ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ P P P P P P R2 ❯ ❯ loop 2 loop 1 node

i1 = i2 +i3 E(t) = R1i1 + 1 C

  • i3 dt

R2i2 − 1 C

  • i3 dt = 0

Bernd Schr¨

  • der

Louisiana Tech University, College of Engineering and Science The Governing Equations of a Multi Loop Circuit