Unit 7 Parallel Circuits

1
Unit 7 Parallel Circuits

• Objectives
• Discuss the characteristics of parallel circuits.
• State the three rules for solving electrical
  values of resistance for parallel circuits.
• Solve the missing values in a parallel circuit
  using the three rules and Ohms law.

2
Unit 7 Parallel Circuits

• Objectives
• Calculate current values using the current
  divider formula.

3
Unit 7 Parallel Circuits

• Three Parallel Circuit Rules
• The voltage drop across any branch is equal to
  the source voltage.
• The total current is equal to the sum of the
  branch currents.
• The total resistance is the reciprocal of the sum
  of the reciprocals of each individual branch.

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Unit 7 Parallel Circuits

• Parallel circuits are circuits that have more
  than one path for current to flow.
• I (total current) 3A 2A 1A 6A

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Unit 7 Parallel Circuits

• Lights and receptacles are connected in parallel.
  Each light or receptacle needs 120 volts.

Panel
6
Unit 7 Parallel Circuits

• The voltage drop across any branch of a parallel
  circuit is the same as the applied (source)
  voltage.

Panel
7
Unit 7 Parallel Circuits

• The voltage drop across any branch of a parallel
  circuit is the same as the source voltage.

E 120 V
E3 120 V
E1 120 V
E2 120 V
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Unit 7 Parallel Circuits

• Parallel Resistance Formulas
• The Reciprocal Formula
• 1/R(total) 1/R1 1/R2 1/R3 1/R(number)
• The Resistors of Equal Value Formula
• R(total) R(any resistor)/N(number of resistors)
• The Product-Over-Sum Formula
• R(total) (R1 x R2) / (R1 R2)

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Unit 7 Parallel Circuits

• The Reciprocal Formula
• The total resistance of a parallel circuit is the
  reciprocal of the sum of the reciprocals of the
  individual branches.
• 1/R(total) 1/R1 1/R2 1/R3 1/R(number)

R(total)
R1
R2
R3
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Unit 7 Parallel Circuits

• Reciprocal Formula Example
• 1/R(total) 1/R1 1/R2 1/R3 1/R(number)
• 1/R(total) 1/50 1/150 1/300 1/100
• R(total) 50 ohms

R(total)50 ?
R1 150 ?
R3 100 ?
R2 300 ?
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Unit 7 Parallel Circuits

• Resistors of Equal Value Formula
• The total resistance of a parallel circuit is
  equal to the value of one resistor, divided by
  the number of resistors.
• R(total) R(any resistor) / N(number of
  resistors)

R(total)
R1
R2
R3
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Unit 7 Parallel Circuits

• Resistors of Equal Value Example
• R(total) R(any resistor)/N(number of resistors)
• R(total) 24(any resistor)/3(number of
  resistors)
• R(total) 24/3 8 ohms

R(total) 8 ?
R1 24 ?
R2 24 ?
R3 24 ?
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Unit 7 Parallel Circuits

• The Product-Over-Sum Formula
• The total resistance of two resistors or branches
  is equal to the value of the product of the
  resistors divided by the sum of resistors.
• R(total) (R1 x R2) / (R1 R2)

R(total)
R1
R2
R3
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Unit 7 Parallel Circuits

• Product Over Sum Formula Example
• Step One
• R(2 3) (R2 x R3) / (R2 R3)
• R(2 3) (30 x 60) / (30 60) 1800 / 90
• R(2 3) 20 ohms

R(total) 10 ?
R2 30 ?
R3 60 ?
R1 20 ?
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Unit 7 Parallel Circuits

• Product-Over-Sum Formula Example
• Step Two
• R(1 2 3) R1 x R(2 3) / R1 R(2 3)
• R(1 2 3) (20 x 20) / (20 20) 400 / 40
  10
• R(1 2 3) 10 ohms R(total)

R(total) 10 ?
R2 30 ?
R3 60 ?
R1 20 ?
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Unit 7 Parallel Circuits

• Product-Over-Sum Formula Review
• The ohm value of two branches is combined.
• This process is repeated using the combined ohm
  value with the next branch.
• When all the branches are combined, this equals
  the total resistance.

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Unit 7 Parallel Circuits

• Current Divider Formula
• I(unknown) I(total) x R(total)/R(unknown)

E3 120 V I3 4 A R3 30 ? P3 360 W
E 120 V I 24 A R 5 ? P 2880 W
E1 120 V I1 8 A R1 15 ? P1 960 W
E2 120 V I2 12 A R2 10 ? P2 120 W
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Unit 7 Parallel Circuits

• Current Divider Formula Example
• I(unknown) I(total) x R(total)/R(unknown)
• Find I1, I2, and I3.

E3 160 V I3 ? A R3 120 ? P3 360 W
E 160 V I 2 A R 80 ? P 320 W
E1 160 V I1 ? A R1 1200 ? P1 960 W
E2 160 V I2 ? A R2 300 ? P2 120 W
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Unit 7 Parallel Circuits

• Current Divider Formula Example
• I(unknown) I(total) x R(total)/R(unknown)
• I1 2 x (80/1200) .133 amps

E 160 V I 2 A R 80 ? P 320 W
E3 160 V I3 ? A R3 120 ? P3 360 W
E1 160 V I1 .133 A R1 1200 ? P1 960 W
E2 160 V I2 ? A R2 300 ? P2 120 W
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Unit 7 Parallel Circuits

• Current Divider Formula Example
• I(unknown) I(total) x R(total)/R(unknown)
• I2 2 x (80/300) .533 amps

E3 160 V I3 ? A R3 120 ? P3 360 W
E 160 V I 2 A R 80 ? P 320 W
E1 160 V I1 .133 A R1 1200 ? P1 960 W
E2 160 V I2 .533 A R2 300 ? P2 120 W
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Unit 7 Parallel Circuits

• Current Divider Formula Example
• I(unknown) I(total) x R(total)/R(unknown)
• I3 2 x (80/120) 1.33 amps

E3 160 V I3 1.33 A R3 120 ? P3 360 W
E 160 V I 2 A R 80 ? P 320 W
E1 160 V I1 .133 A R1 1200 ? P1 960 W
E2 160 V I2 .5 A R2 300 ? P2 120 W
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Unit 7 Parallel Circuits

• Review
• Parallel circuits have more than one circuit path
  or branch.
• The total current is equal to the sum of the
  branch currents.
• The voltage drop across any branch is equal to
  the source voltage.
• The total resistance is less than any branch
  resistance.

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Unit 7 Parallel Circuits

• Review
• The total resistance can be found using the
  reciprocal formula.
• The product-over-sum formula and the resistors of
  equal value formula are special formulas.
• Circuits in homes are connected in parallel.

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Unit 7 Parallel Circuits

• Review
• The total power is equal to the sum of the
  resistors power.
• Parallel circuits are current dividers.
• The amount of current flow through each branch of
  a parallel circuit is inversely proportional to
  its resistance.