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 Ohm’s law.

2. 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.

3. 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

4. Unit 7 Parallel Circuits
Lights and receptacles are connected in parallel. Each light or receptacle needs 120 volts.
Panel

5. Unit 7 Parallel Circuits
The voltage drop across any branch of a parallel circuit is the same as the applied (source) voltage.
Panel

6. 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

7. 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)

8. 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

9. 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
R(total)50 Ω R1
150 Ω R2
300 Ω R3
100 Ω

10. 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

11. 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 Ω R1
24 Ω R2
24 Ω R3
24 Ω

12. 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

13. 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
R(total)
10 Ω R1
20 Ω R2
30 Ω R3
60 Ω

14. 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)
R(total)
10 Ω R1
20 Ω R2
30 Ω R3
60 Ω

15. 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.

16. 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.

17. Unit 7 Parallel Circuits
Review:
The product-over-sum formula and the resistors of equal value formula are special formulas.
Circuits in homes are connected in parallel.

18. Unit 7 Parallel Circuits
Review:
Parallel circuits are current dividers.
The amount of current flow through each branch of a parallel circuit is inversely proportional to its resistance.