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.
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
Unit 7 Parallel Circuits
Lights and receptacles are connected in parallel.
Each light or receptacle needs 120 volts.
Panel
Unit 7 Parallel Circuits
The voltage drop across any branch of a parallel
circuit is the same as the applied (source) voltage.
Panel
Unit 7 Parallel Circuits
The voltage drop across any branch of a parallel
circuit is the same as the source voltage.
E3 = 120 V
E = 120 V
E1 = 120 V
E2 = 120 V
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)
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
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 Ω
R1
150 Ω
R2
300 Ω
R3
100 Ω
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
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)
8Ω
R1
24 Ω
R2
24 Ω
R3
24 Ω
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
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 Ω
R1
20 Ω
R2
30 Ω
R3
60 Ω
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 Ω
R1
20 Ω
R2
30 Ω
R3
60 Ω
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.
Unit 7 Parallel Circuits
Current Divider Formula
I (unknown) = I (total) x R (total)/ R (unknown)
E3 = 120 V
I3 = 4 A
R3 = 30 Ω
P3 = 360 W
E = 120 V
I = 24 A
R=5Ω
P = 2880 W
E1 = 120 V
I1 = 8 A
R1 = 15 Ω
P1 = 960 W
E2 = 120 V
I2 = 12 A
R2 = 10 Ω
P2 = 120 W
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=2A
R = 80 Ω
P = 320 W
E3 = 160 V
I3 = ? A
R3 = 120 Ω
P3 = 360 W
E1 = 160 V
I1 = ? A
R1 = 1200 Ω
P1 = 960 W
E2 = 160 V
I2 = ? A
R2 = 300 Ω
P2 = 120 W
Unit 7 Parallel Circuits
Current Divider Formula Example
I (unknown) = I (total) x R (total)/R (unknown)
I1 = 2 x (80/1200) = .133 amps
E3 = 160 V
I3 = ? A
R3 = 120 Ω
P3 = 360 W
E = 160 V
I=2A
R = 80 Ω
P = 320 W
E1 = 160 V
I1 = .133 A
R1 = 1200 Ω
P1 = 960 W
E2 = 160 V
I2 = ? A
R2 = 300 Ω
P2 = 120 W
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=2A
R = 80 Ω
P = 320 W
E3 = 160 V
I3 = ? A
R3 = 120 Ω
P3 = 360 W
E1 = 160 V
I1 = .133 A
R1 = 1200 Ω
P1 = 960 W
E2 = 160 V
I2 = .533 A
R2 = 300 Ω
P2 = 120 W
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=2A
R = 80 Ω
P = 320 W
E3 = 160 V
I3 = 1.33 A
R3 = 120 Ω
P3 = 360 W
E1 = 160 V
I1 = .133 A
R1 = 1200 Ω
P1 = 960 W
E2 = 160 V
I2 = .5 A
R2 = 300 Ω
P2 = 120 W