Series and Parallel CircuitsWhen devices are connected in an electric circuits, they can be connected in “series” or in “parallel” with other devices.

1 2A B

The devices, numbered “1” and “2” in the diagram above, are connected in series. If an electron (or even conventional positive current) needs to move from point A to point B, it must go through both device 1 and device 2. Everything that goes through one must also go through the other.

When devices are series, any current that goes through one device must also go through the other devices. For example:

Series Connection

Series and Parallel CircuitsWhen devices are connected in an electric circuits, they can be connected in “series” or in “parallel” with other devices.

The devices, numbered “1” and “2” in the diagram above, are connected in parallel. If an electron (or even conventional positive current) needs to move from point A to point B, it must go through only one device, not both. Some current goes through one, some through the other.

When devices are parallel, the current goes through one device only. For example:

Parallel Connection

1

2A B

If devices 1 and 2 are resistors, think of the series connection as a longer resistor. Longer resistors have greater resistance. The total resistance of a combination of resistors in series is

greater than any of the individual resistances.

1 2A B

Resistors in Series

1

2A B

Resistors in Parallel

If devices 1 and 2 are resistors, think of the parallel connection as a wider resistor. Wider resistors have lower

resistance. The total resistance of a combination of resistors in paralle is smaller than any of the individual resistances.

Series Circuits

V R2

R1

R3

The schematic circuit diagram to the right shows three resistors (R) connected in series with a source of potential difference (V).

Rules for a simple series circuit…. (in sentence form)

1) The total equivalent resistance of resistors in series is equal to the sum of the individual resistances.

2) The sum of the voltage drops across each of the resistors is equal to the total voltage of the power supply.

3) The same amount of current flows through all the resistors.

4) The total power converted by the three resistors is equal to the sum of the individual powers

Series Circuits

V R2

R1

R3

The schematic circuit diagram to the right shows three resistors (R) connected in series with a source of potential difference (V).

Rules for a simple series circuit…. (in equation form)

Req = R1 + R2 + R3 +...

V = V1 + V2 + V3 + ...

I = I1 = I2 = I3 = ...

P = P1 + P2 + P3 + ...

Parallel Circuits

The schematic circuit diagram to the right shows three resistors (R) connected in parallel with a source of potential difference (V).

Rules for a simple parallel circuit…. (in sentence form)

1) The reciprocal of the total equivalent resistance of resistors in series is equal to the sum of the reciprocals of the individual resistances.

2) All of the resistors have the same voltage drop across them.

3) The sum of the currents through all the parallel resistors is equal to the total current supplied by the voltage source.

4) The total power converted by the three resistors is equal to the sum of the individual powers.

R3V R1 R2

Parallel Circuits

The schematic circuit diagram to the right shows three resistors (R) connected in parallel with a source of potential difference (V).

V = V1 = V2 = V3 = ….

I = I1 + I2 + I3 +….

P = P1 + P2 + P3 + ….

Rules for a simple parallel circuit…. (in equation form)

R3V R1 R2

Series Circuits: Example Problem

V = 24 VR2 = 4

R1 = 2

R3 = 6

Req = R1 + R2 + R3 +…

V = V1 + V2 + V3 + …

I = I1 = I2 = I3 = …

P = P1 + P2 + P3 + ...

4

8

12

2

2

2

1

V I R P

2

3

T

2

4

6

24 2 12

8

16

24

48

Fill in Given

Use Req = R1 + R2 + R3 +… to find the total equivalent resistance.

Use V = IR to find the total current

I = I1 = I2 = I3 = …

Use V = IR to find the individual voltages

Use P = VI to find all the powers

Parallel Circuits: Example Problem

50

50

50

1

V I R P

2

3

T

20

25

100

50

2.5

2

0.5

5 10

125

100

25

250

Fill in Given

V = V1 = V2 = V3 = ...

Use V = IR to find the individual currents

Use P = VI to find all the powers

V = V1 = V2 = V3 = ...

I = I1 + I2 + I3 + ...

P = P1 + P2 + P3 = ...

V = 50 V R1 =20

R2 =25

R3 =100

Use to find the total equivalent resistance.

Combination Circuits

The circuit to the right is a complicated combination circuit. The resistors aren’t all in series or all in parallel.

To analyze a combination circuit, first look for pairs (or more) of resistors which are in series or parallel. In this example R3 and R4 are in series, while R5 and R6 are in parallel. Use the series and parallel rules to replace the pairs with

“equivalent” resistors.

R3

V

R1

R2

R4R6

R5

V

R1

R2

R4, 3

R5, 6

V

R1

R2, 3, 4

R5, 6

V R1, 2, 3, 4, 5, 6

Now R2, 3, 4 is in series with R1 and R5, 6.

Now R2 is in parallel with R4, 3.

Combination Circuits

R3 = 12

V = 120 V

R1 = 19

R2 =

48 R4 = 12

R6 = 30

R5 = 6

Example: Find the equivalent resistance of the six resistors in the circuit at right.

1/R5,6 = 1/R5 + 1/R6 = 1/30 + 1/6 R5,6 = 5

R3,4 = R3 + R4 = 12 + 12 R3,4 = 24

1/R2,3,4 = 1/R2 + 1/R3,4 = 1/48 + 1/24R2,3,4 = 16

R1,2,3,4,5,6 = R1 + R2,3,4 + R5,6

R1,2,3,4,5,6 = 19 + 16 + 5 R1,2,3,4,5,6 = 40

Combination Circuits: Finding Equivalent ResistanceR2R1

R4

R5R3

R6

R8 R7

R1

R4

R5R3

R2,6

R8 R7

R1

R4

R2,5,6R3

R8 R7

R1

R4

R3

R8 R2,5,6,7

R1

R2,4,5,6,7

R3

R8

R1,2,4,5,6,7

R3

R8

R1,2,3,4,5,6,7

R8

R1,2,3,4,5,6,7,8

Combination Circuits: Hints

R2R1

A

B

When the current reaches point A, it must split to the right or the left. If R1 has a bigger resistance than R2, most of the current will go through R2.

If R1 = 2 x R2, then twice as much current will go through R2 as compared to R1.

I1 + I2 = I

2 x I1 = I2

I1 = (1/3)I

I2 = (2/3)I

Answer:

If R1 = 5 x R2, then five times as much current will go through R2 as compared to R1.

I1 + I2 = 30 A

5 x I1 = I2

I1 = (1/6)(30 A) = 5 A

I2 = (5/6)(30 A) = 25 A

R1 = 50 R2= 10

A

B

I = 30 AExample Problem:

How much of the 30 A of current goes through each resistor in the diagram at right?

Combination CircuitsExample Problem:

The circuit to the right represents a battery and four identical light bulbs connected in a combination circuit.

Q: Put them in order from brightest to dimmest:

Brightest: R4 (all current goes through it)

2nd R1 (gets 2/3 of total current)

3rd & 4th R2 and R3 (get 1/3 of total current)

R2R1

R3

R4

Combination CircuitsNow the bulb represented by R3 is unscrewed from its socket. R2R1

R3

R4

Q: What happens to the brightness of the other three bulbs?

R2 goes out (no current through that branch)

R4 gets dimmer (fewer current paths = more total resistance in circuit = less total current = less through R4)

R1 gets brighter (current through R4 decreases, voltage across R4 decreases, voltage across R1 increases = it gets less bright)

Combination Circuits

R3V

R1

R2

R4R6

R5

R7

R8

R9

R10

The circuit to the right consists of ten identical resistors. Put the resistors in order from the greatest amount of current to the least current.

Answer:

Most current: R1 (only resistor which all the current passes through)

2nd: R2 (gets 2/3 of the total current)

3rd: R5 and R6 (get 1/2 of the total current)

4th: R3 and R4 (get 1/3 of the total current)

Last: R7, R8, R9, R10 (get 1/4 of total current)