DifferencesDifferencesBetweenBetween

SeriesSeriesandand

ParallelParallelCircuitsCircuits

Series ParallelSeries Parallel

ET = E1 + E2 + E3 +…

RT = R1 + R2 + R3 + …

IT = I1 = I2 = I3 = …

PT = P1 + P2 + P3 + …

ET = E1 = E2 = E3 = …..

Voltage relationship in a Parallel CircuitVoltage relationship in a Parallel Circuit

24 V

R1 R3R2

12 24 48

The top of each resistor is The top of each resistor is connected to the same connected to the same potential - + terminal of the potential - + terminal of the

DC Supply.DC Supply. The bottom of each resistor The bottom of each resistor

is connected to the same is connected to the same potential - - Terminal of the potential - - Terminal of the DC Supply.DC Supply.

Each Load (or Resistor) has Each Load (or Resistor) has the same potential applied.the same potential applied.

Series ParallelSeries Parallel

ET = E1 + E2 + E3 +…

IT = I1 = I2 = I3 = …

RT = R1 + R2 + R3 + …

PT = P1 + P2 + P3 + …

ET = E1 = E2 = E3 = …..

IT = I1 + I2 + I3 + …

Current in a Parallel CircuitCurrent in a Parallel Circuit

24 V

R1 R3R2

12 24 48I =2A1

24 V

R1 R3R2

12 24 48I =2A1 I =1A2

24 V

R1 R3R2

12 24 48I =.5A3I =2A1 I =1A2

24 V

R1 R3R2

12 24 48I =.5A3I =2A1 I =1A2

I = 3.5AT

Circuit Current in a ParallelCircuit Current in a Parallel

24 V

R1 R3R2

12 24 48I =.5A3I =2A1 I =1A2

0.5A1.5A3.5A

3.5A 1.5A 0.5A The Sum of the currents entering The Sum of the currents entering a point is equal to the sum of a point is equal to the sum of currents leaving that point:currents leaving that point:

E.g. – 3.5A leaves the DC Power E.g. – 3.5A leaves the DC Power Supply and arrives at the first Supply and arrives at the first node (where R1 is connected); 2A node (where R1 is connected); 2A travels through R1; the remaining travels through R1; the remaining 1.5A travels to R2 and R3. From 1.5A travels to R2 and R3. From the top side of the resistors, the the top side of the resistors, the current entering a point is equal to current entering a point is equal to the sum of the currents entering a the sum of the currents entering a point.point.

Series ParallelSeries Parallel

ET = E1 + E2 + E3 +…

IT = I1 = I2 = I3 = …

RT = R1 + R2 + R3 + …

PT = P1 + P2 + P3 + …

ET = E1 = E2 = E3 = …..

IT = I1 + I2 + I3 + …

1/RT = 1/R1 + 1/R2 + 1/R3 +..

Parallel ResistanceParallel Resistance

24 V

R1 R3R2

12 24 48I =.5A3I =2A1 I =1A2

I = 3.5AT

R = E /IR = 24V/3.5AR = 6.86

T T T

T

T

Using the Ohm’s Law Formula Using the Ohm’s Law Formula (R = E/I), the resistance that (R = E/I), the resistance that the Power Source detects is the Power Source detects is equal to 6.86 equal to 6.86 ΩΩ..

Each resistor is called a Each resistor is called a branch.branch.

Parallel ResistanceParallel Resistance

24 V

R1 R3R2

12 24 48

I =.5A3I =2A1 I =1A2I = 3.5AT

R = E /IR = 24V/3.5AR = 6.86

T T T

T

T 1/RT = 1/R1 + 1/R2 + 1/R31/RT = 1/12 + 1/24 + 1/481/RT = (4 + 2 + 1)/48 = 7/487 RT = 48RT = 48/7RT = 6.86

Using the Reciprocal Formula, Using the Reciprocal Formula, the Total Resistance equals the Total Resistance equals 6.866.86ΩΩ, the same value arrived , the same value arrived at by using the R = E/I at by using the R = E/I formula.formula.

NOTE: the total resistance of NOTE: the total resistance of the circuit is always lower than the circuit is always lower than the lowest branch resistance. the lowest branch resistance.

Parallel ResistanceParallel Resistance

A Scientific Calculator can be A Scientific Calculator can be used to solve for the total used to solve for the total resistance in a parallel circuit.resistance in a parallel circuit.

Using a Calculator(Enter)12 (R1 value)

1/x (or X )

+

(Enter)24 (R2 value)

1/x

+(Enter)48 (R3 value)

1/x=

1/x=

6.86

- 1

24 V

R1 R3R2

12 24 48I =.5A3I =2A1 I =1A2

I = 3.5AT

R = E /IR = 24V/3.5AR = 6.86

T T T

T

T

Parallel ResistanceParallel Resistance

24 V

R1 R3R2

12 24 48I =.5A3I =2A1 I =1A2

I = 3.5AT

R = E /IR = 24V/3.5AR = 6.86

T T T

T

T

R =(1+2)

R1 x R2R1 + R212 x 2412 + 24

288368

R =(1+2)

R =(1+2)

R =(1+2)

24 V

R1 R3R2

12 24 48I =.5A3I =2A1 I =1A2

I = 3.5AT

R = E /IR = 24V/3.5AR = 6.86

T T T

T

T

If only two resistors are in If only two resistors are in parallel, the Product over the parallel, the Product over the Sum can be used.Sum can be used.

In the example, two resistors In the example, two resistors are used and the resultant are used and the resultant resistance value replaces the resistance value replaces the two resistors.two resistors.

Then, the resultant value and Then, the resultant value and the value of R3 can be used; the value of R3 can be used; the answer still comes up as the answer still comes up as 6.86 6.86 ΩΩ..

Series ParallelSeries Parallel

ET = E1 + E2 + E3 +…

IT = I1 = I2 = I3 = …

RT = R1 + R2 + R3 + …

PT = P1 + P2 + P3 + …

ET = E1 = E2 = E3 = …..

IT = I1 + I2 + I3 + …

1/RT = 1/R1 + 1/R2 + 1/R3 +..

PT = P1 + P2 + P3 + …..

Parallel PowerParallel Power

24 V

R1 R3R2

12 24 48

I =.5A3I =2A1 I =1A2I = 3.5AT

R = 6.86T

24W 12W48W

P = I x EP = 3.5A x 24VP = 84W

T T T

T

T

P = P + P + PP = 48W + 24W + 12WP = 84W

T 1 2 3

T

T

The Total Power is the sum of The Total Power is the sum of the power consumed in each the power consumed in each branch. branch.