Unit 8 Combination Circuits

1
Unit 8 Combination Circuits

• Objectives
• Define a combination circuit.
• List the rules for parallel circuits.
• List the rules for series circuits.
• Solve for combination circuit values.

2
Unit 8 Combination Circuits

• Characteristics
• There are multiple current paths.
• Resistors may be in series or parallel with other
  resistors.
• A node is where three or more paths come
  together.
• The total power is the sum of the resistors
  power.

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Unit 8 Combination Circuits

• A simple combination circuit.

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Unit 8 Combination Circuits

• Solving Combination Circuits

E1 ? V I1 ? A R1 325 ?
E3 ? V I3 ? A R3 150 ?
E ? V I 1 A R ? ?
E2 ? V I2 ? A R2 275 ?
E4 ? V I4 ? A R4 250 ?
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Unit 8 Combination Circuits

• Series Circuit Rules
• The current is the same at any point in the
  circuit.
• The total resistance is the sum of the individual
  resistances.
• The sum of the voltage drops or the individual
  resistors must equal the applied (source)
  voltage.

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Unit 8 Combination Circuits

• Parallel Circuit Rules
• The voltage across any circuit branch is the same
  as the applied (source) voltage.
• The total current is the sum of the current
  through all of the circuit branches.
• The total resistance is equal to the reciprocal
  of the sum of the reciprocals of the branch
  resistances.

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Unit 8 Combination Circuits

• Simplifying the Circuit
• Resistors in series can be combined to form an
  equivalent resistance.
• Resistors in parallel can be combined to form an
  equivalent resistance.
• The equivalent resistances are used to draw
  simplified equivalent circuits.

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Unit 8 Combination Circuits

• Reducing Combination Circuits
• Combine R1 R2, and R3 R4.

R3 150 ?
R1 325 ?
R ? ?
R4 250 ?
R2 275 ?
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Unit 8 Combination Circuits

• Reducing Combination Circuits
• Redraw simplified circuit.
• R1 R2 R12 600 ohms
• R3 R4 R34 400 ohms

R12 600 ?
R34 400 ?
R ? ?
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Unit 8 Combination Circuits

• Solving Combination Circuits
• Solve for the applied voltage using Ohms law.
• Note that the I(total) was given data.
• E(source) I(total) x R(total) 1 x 240 240 V

E 240 V I 1 A R 240 ?
R12 600 ?
R34 400 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits
• Solve for the branch currents using Ohms law.
• E(source) E12 E34
• I12 E12 / R12 240/600 0.4 A

E 240 V I 0.4 A R12 600 ?
E 240 V I 1 A R 240 ?
R34 400 ?
12
Unit 8 Combination Circuits

• Solving Combination Circuits
• Solve for the branch currents using Ohms law.
• E(source) E12 E34
• I34 E34 / R34 240/400 0.6 A

E12 240 V I 0.4 A R12 600 ?
E34 240 V I 0.6 A R34 400 ?
E 240 V I 1 A R 240 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits
• Expand the circuit back to the original circuit.
• Branch currents remain the same.

E1 ? V I1 0.4 A R1 240 ?
E3 ? V I3 0.6 A R3 240 ?
E 240 V I 1 A R 240 ?
E4 ? V I4 0.6 A R4 240 ?
E2 ? V I2 0.4 A R2 240 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits
• Solve for each voltage drop using Ohms law.
• E1 I1 x R1 0.4 x 325 130 V

E1 130 V I1 0.4 A R1 325 ?
E3 ? V I3 0.6 A R3 150 ?
E 240 V I 1 A R 240 ?
E4 ? V I4 0.6 A R4 250 ?
E2 ? V I2 0.4 A R2 275 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits
• Solve for each voltage drop using Ohms law.
• E2 I2 x R2 0.4 x 275 110 V

E1 130 V I1 0.4 A R1 325 ?
E3 ? V I3 0.6 A R3 150 ?
E 240 V I 1 A R 240 ?
E4 ? V I4 0.6 A R4 250 ?
E2 110 V I2 0.4 A R2 275 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits
• Solve for each voltage drop using Ohms law.
• E3 I3 x R3 0.6 x 150 90 V

E1 130 V I1 0.4 A R1 325 ?
E3 90 V I3 0.6 A R3 150 ?
E 240 V I 1 A R 240 ?
E4 ? V I4 0.6 A R4 250 ?
E2 110 V I2 0.4 A R2 275 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits
• Solve for each voltage drop using Ohms law.
• E4 I4 x R4 0.6 x 250 150 V

E1 130 V I1 0.4 A R1 325 ?
E3 90 V I 3 0.6 A R3 150 ?
E 240 V I 1 A R 240 ?
E4 150 V I4 0.6 A R4 250 ?
E2 110 V I2 0.4 A R2 275 ?
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Unit 8 Combination Circuits

• Kirchhoffs Laws
• The algebraic sum of the voltage sources and
  voltage drops in a closed circuit must equal
  zero. This law states that the sum of the voltage
  drops in a series circuit must equal the applied
  voltage.
• The algebraic sum of the current entering and
  leaving a point must equal zero. The second law
  is for parallel circuits and states that the
  total current is the sum of all the branch
  currents.

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Unit 8 Combination Circuits

• Solving Combination Circuits Review

E1 ? V I1 ? A R1 325 ?
E3 ? V I3 ? A R3 150 ?
E ? V I 1 A R ? ?
E2 ? V I2 ? A R2 275 ?
E4 ? V I4 ? A R4 250 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Combine R1 R2, and R3 R4

R3 150 ?
R1 325 ?
R ? ?
R4 250 ?
R2 275 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Redraw simplified circuit.
• R1 R2 R12 600 ohms
• R3 R4 R34 400 ohms

R12 600 ?
R34 400 ?
R ? ?
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Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Solve for the applied voltage using Ohms Law.
• Note that the I(total) was given data.
• E(source) I(total) x R(total) 1 x 240 240 V

E 240 V I 1 A R 240 ?
R12 600 ?
R34 400 ?
23
Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Solve for the branch currents using Ohms law.
• E(source) E12 E34
• I12 E12 / R12 240/600 0.4 A

E 240 V I 1 A R 240 ?
E 240 V I 0.4 A R12 600 ?
R34 400 ?
24
Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Solve for the branch currents using Ohms law.
• E(source) E12 E34
• I34 E34 / R34 240/400 0.6 A

E 240 V I 1 A R 240 ?
E12 240 V I 0.4 A R12 600 ?
E34 240 V I 0.6 A R34 400 ?
25
Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Expand the circuit back to the original circuit.
• Branch currents remain the same.

E1 ? V I1 0.4 A R1 240 ?
E3 ? V I3 0.6 A R3 240 ?
E 240 V I 1 A R 240 ?
E4 ? V I4 0.6 A R4 240 ?
E2 ? V I2 0.4 A R2 240 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Solve for each voltage drop using Ohms law.
• E1 I1 x R1 0.4 x 325 130 V

E1 130 V I1 0.4 A R1 325 ?
E3 ? V I3 0.6 A R3 150 ?
E 240 V I 1 A R 240 ?
E4 ? V I4 0.6 A R4 250 ?
E2 ? V I2 0.4 A R2 275 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Solve for each voltage drop using Ohms law.
• E2 I2 x R2 0.4 x 275 110 V

E1 130 V I1 0.4 A R1 325 ?
E3 ? V I3 0.6 A R3 150 ?
E 240 V I 1 A R 240 ?
E4 ? V I4 0.6 A R4 250 ?
E2 110 V I2 0.4 A R2 275 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Solve for each voltage drop using Ohms law.
• E3 I3 x R3 0.6 x 150 90 V

E1 130 V I1 0.4 A R1 325 ?
E3 90 V I3 0.6 A R3 150 ?
E 240 V I 1 A R 240 ?
E4 ? V I4 0.6 A R4 250 ?
E2 110 V I2 0.4 A R2 275 ?
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Unit 8 Combination Circuits

• Solving Combination Circuits Review
• Solve for each voltage drop using Ohms law.
• E4 I4 x R4 0.6 x 250 150 V

E1 130 V I1 0.4 A R1 325 ?
E3 90 V I3 0.6 A R3 150 ?
E 240 V I 1 A R 240 ?
E4 150 V I4 0.6 A R4 250 ?
E2 110 V I2 0.4 A R2 275 ?
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Unit 8 Combination Circuits

• Review
• The three rules for series circuits are
• The current is the same at any point in the
  circuit.
• The total resistance is the sum of the individual
  resistances.
• The applied voltage is equal to the sum of the
  voltage drops across the individual components.

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Unit 8 Combination Circuits

• Review
• The three rules for parallel circuits are
• The total voltage is the same as the voltage
  across any branch.
• The total current is the sum of the individual
  currents.
• The total resistance is the reciprocal of the sum
  of the reciprocals of the branch resistances.

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Unit 8 Combination Circuits

• Review
• Combination circuits are circuits that contain
  both series and parallel branches.
• A node is where three or more paths come
  together.
• The total power is the sum of all the circuit
  resistors power.

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Unit 8 Combination Circuits

• Review
• When solving combination circuits, simplify,
  reduce, and redraw equivalent value circuits.
• Apply the series rules and the parallel rules
  selectively to various parts of the combination
  circuit.