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Combined Series and Parallel Circuits. Objectives: Calculate the equivalent resistance, current, and voltage of series and parallel circuits. Calculate the equivalent resistance of circuits combining series and parallel connections.

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Combined Series and Parallel Circuits


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combined series and parallel circuits

Combined Series and Parallel Circuits

Objectives:

Calculate the equivalent resistance, current, and voltage of series and parallel circuits.

Calculate the equivalent resistance of circuits combining series and parallel connections.

To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit problem.

Solve circuit problems.

resistance and current
Resistance and Current

Series Circuit

Equivalent resistance is equal to the sum of all the resistance in the circuit.

Circuit current is equal to the voltage source divided by the equivalent resistance.

resistance and current1
Resistance and Current

Parallel Circuit

The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.

The total current is the sum of all the currents.

The potential difference across each resistor is the same

household circuits

Household Circuits

Small resistance from wiring

Why do the lights dim when the hair dryer goes on?

This is called a combination series and parallel circuit

series and parallel circuits
Series and Parallel Circuits
  • Draw a diagram of the circuit
  • Find any resistors in parallel. They must have the same potential difference across them. Calculate the single equivalent resistance of a resistor that can replace them.
  • Are any resistors (including the parallel equivalent resistor) in series? Resistors in series have one and only one current path through them. Calculate the new single equivalent resistance that can replace them. Draw a new schematic diagram using that resistor.
  • Repeat steps 2 and 3 until you can reduce the current to a single resistor. Find the total circuit current. Then go backwards to find the currents through and the voltages across individual resistors.
kirchhoff s rules gustav kirchhoff 1845
Kirchhoff’s RulesGustav Kirchhoff - 1845
  • The sum of the currents entering any junction must equal the sum of the currents leaving that junction. (junction rule)
  • The sum of the potential differences across all the elements around any closed circuit loop must equal zero. (loop rule)
now lets try some problems

Now lets try some problems

Don’t wait to get totally lost. Ask your questions as they come to you.

slide10
#1

Series Circuit

Rt = R1 + R2 + R3 + …

Rt = 4 + 6 + 3 + 1 =

14 

I = V  R

I = 40  14 =

2.86 amps

slide11
#2

Series Circuit

Rt = R1 + R2 + R3 + …

Rt = 5 + 4 + 12 =

21 

I = V  R

I = 10  21 =

0.476 amps

slide12
#3

Series Circuit

Rt = R1 + R2 + R3 + …

Rt = 3 + 1 + 7 =

11 

I = V  R

I = 120  11 =

10.9 amps

slide13
#4

Series Circuit

Rt = R1 + R2 + R3 + …

Rt = 5 + 1 + 6 + 3 + 4 + 1 =

20 

I = V  R

I = 9  20 =

0.45 amps

slide14
#5

Series Circuit

Rt = R1 + R2 + R3 + …

Rt = 12 + 20 + 5 =

37 

I = V  R

I = 60  37 =

1.62 amps

slide15
#6

Parallel Circuit

1/Rt = 1/R1 + 1/R2 + 1/R3 + …

1/Rt = 1/2 + 1/2 + 1/2 = 1.5

Rt = 0.667 

I = V  R

I = 6  0.667 =

9.00 amps

slide16
#7

Parallel Circuit

1/Rt = 1/R1 + 1/R2 + 1/R3 + …

1/Rt = 1/6 + 1/8 + 1/4 = 0.542

Rt = 1.85 

I = V  R

I = 120  1.85 =

64.9 amps

slide17
#8

Parallel Circuit

1/Rt = 1/R1 + 1/R2 + 1/R3 + …

1/Rt =1/2.5 + 1/6 + 1/1 = 1.57

Rt = 0.638 

I = V  R

I = 14  0.638 =

21.9 amps

now let s put em together

Now let’s put ‘em together

Simplify diagram in steps to a single resistor

Calculate total resistance and current for the whole circuit

Then work backwards to find voltages and currents at individual resistors

It takes time and care to do this right

DON’T TRY TO RUSH THROUGH IT!

slide19
#9

The 2  and 3  resistors are in series with one another

They combine to form a 5  resistor

slide20

The three resistors are hooked up in parallel with each other.

1/Rt = 1/R1 + 1/R2 + 1/R3 + …

1/Rt =1/5 + 1/1 + 1/6 = 1.37

Rt = 0.730 

The circuit now looks like this

I = V/R = 120/.730 =

I = 164 amps

slide21
#10

Combine the 3  and the 7  resistors that are in series with one another to make a 10  resistor

Combine the 1  and the 2  resistor that are in series with one another to make a 3  resistor

Then re-draw the circuit

It should look like this

slide22

The three resistors are hooked up in parallel with each other.

1/Rt = 1/R1 + 1/R2 + 1/R3 + …

1/Rt =1/10 + 1/4 + 1/3 = 0.683

Rt = 1.46 

The circuit now looks like this

I = V/R = 40/1.46 =

I = 27.4 amps

slide23
#11

Combine the resistors hooked up in series with one another and re-draw the circuit

It should look like this

slide24

The three resistors are hooked up in parallel with each other.

1/Rt = 1/R1 + 1/R2 + 1/R3 + …

1/Rt =1/4 + 1/4 + 1/10 = 0.600

Rt = 1.67 

The circuit now looks like this

I = V/R = 220/1.67 =

I = 132 amps

slide25
#12

What type of circuit is this?

Find the total resistance

Find the total current

The ___________ is the same for all devices in a series circuit

Therefore I3 =

To find V2 we need to know…

V = IR so V2 = 1.17(4)

Series

12 

1.17 amps

Current

1.17 amps

R2 and I2

4.68 V

slide26
#13

What type of circuit is this?

Find the total resistance

Find the total current

The ___________ is the same for all lines in a parallel circuit

Therefore V3 =

To find I3 we need to know…

I = V/R so I3 = 120(2.5)

Parallel

1.11 

108 amps

Voltage

120 V

V3 & R3

48 amps

slide27
#14

Both

Is this a series or a parallel circuit?

Combine the resistors in series first.

Then re-draw the circuit.

It should look something like this

slide28

Now find the total resistance

Do we need the total current? If so, what is it?

How is resistor #5 hooked up?

Those two resistors combine to form a resistor that is _____ 

How is that 5  resistor hooked up to the circuit?

2.4 

No

In series with #6

5 

In parallel with the other combined resistors

more about resistor 5
More about Resistor #5

What is the same for all the lines in a parallel circuit?

What is the voltage across the 5  resistor?

What is the current through that 5  resistor?

What is the current through resistor #5?

Why?

V = IR V = 22(3)

Voltage

110 V

22 amps

22 amps

Series w/ #6

66 V

let s look at resistor 4
Let’s look at Resistor #4

How is resistor #4 hooked up?

Those two resistors combine to form a resistor that is __ 

How is that 11  resistor hooked up to the circuit?

What is the same for all the lines in a parallel circuit?

What is the voltage across the 11  resistor?

In series with #3

11 

Parallel with the other combined resistors

Voltage

110 V

more about resistor 4
More about Resistor #4

What is the current through that 11  resistor?

What is the current through resistor #4?

Why?

10 amps

10 amps

Series w/ #3

slide32

Now move on to the rest of the packet.

We have the answers at all the problems.

We have the solutions to #17 - #22.

#23 is extra credit (it is really hard)