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**Unit 7 Parallel Circuits**

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**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 Ohm’s law. Calculate current values using the current divider formula.

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**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 Figure 7-1

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**Unit 7 Parallel Circuits**

Lights and receptacles are connected in parallel. Each light or receptacle needs 120 volts. Panel 7-3

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**Unit 7 Parallel Circuits**

The voltage drop across any branch of a parallel circuit is the same as the applied (source) voltage. Panel 7-3

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**Unit 7 Parallel Circuits**

The voltage drop across any branch of a parallel circuit is the same as the source voltage. E = 120 V Figure 7-4 with the values removed 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) Figure 7-4 with existing text removed and new text inserted 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/ / /100 R (total) = 50 ohms Figure 7-4 with existing text removed and new text inserted Or Figure 7-10 R(total)50 Ω R1 150 Ω R2 300 Ω R3 100 Ω

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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) Figure 7-4 with existing text removed and new text inserted 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 Figure 7-4 with existing text removed and new text inserted Or figure 7-6 R (total) 8 Ω R1 24 Ω R2 24 Ω R3 24 Ω

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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) Figure 7-4 with existing text removed and new text inserted 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) / ( ) = 1800 / 90 R(2 & 3) = 20 ohms Figure 7-4 with existing text removed and new text inserted Or Figure 7-7 R (total) 10 Ω R1 20 Ω R2 30 Ω R3 60 Ω

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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) / ( ) = 400 / 40 = 10 R(1 & 2 & 3) = 10 ohms = R (total) Figure 7-4 with existing text removed and new text inserted Or Figure 7-7 R (total) 10 Ω R1 20 Ω R2 30 Ω R3 60 Ω

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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) E = 120 V I = 24 A R = 5 Ω P = 2880 W E3 = 120 V I3 = 4 A R3 = 30 Ω P3 = 360 W Figure 7-4 with existing text removed and new text inserted E1 = 120 V I1 = 8 A R1 = 15 Ω P1 = 960 W E2 = 120 V I2 = 12 A R2 = 10 Ω 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. E = 160 V I = 2 A R = 80 Ω P = 320 W E3 = 160 V I3 = ? A R3 = 120 Ω P3 = 360 W Figure 7-4 with existing text removed and new text inserted E1 = 160 V I1 = ? A R1 = 1200 Ω P1 = 960 W E2 = 160 V I2 = ? A R2 = 300 Ω 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 Ω P = 320 W E3 = 160 V I3 = ? A R3 = 120 Ω P3 = 360 W Figure 7-4 with existing text removed and new text inserted E1 = 160 V I1 = .133 A R1 = 1200 Ω P1 = 960 W E2 = 160 V I2 = ? A R2 = 300 Ω 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 E = 160 V I = 2 A R = 80 Ω P = 320 W E3 = 160 V I3 = ? A R3 = 120 Ω P3 = 360 W Figure 7-4 with existing text removed and new text inserted E1 = 160 V I1 = .133 A R1 = 1200 Ω P1 = 960 W E2 = 160 V I2 = .533 A R2 = 300 Ω 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 E = 160 V I = 2 A R = 80 Ω P = 320 W E3 = 160 V I3 = 1.33 A R3 = 120 Ω P3 = 360 W Figure 7-4 with existing text removed and new text inserted E1 = 160 V I1 = .133 A R1 = 1200 Ω P1 = 960 W E2 = 160 V I2 = .5 A R2 = 300 Ω 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.

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