Electric Circuits

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Do Light Bulb Demo

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Electric CircuitsThere are two different types of electrical circuits.

and

Series Parallel

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One Path

More than 1 path

Series Circuit:Circuit in which a current flows through each component, one after another. There is only one path for the current to follow.

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Because there is only one path for electrons to travel in a series circuit. The current at any one point in the circuit would be equal to the current at any other point in the circuit.

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1 2 3 ....TI I I I

The current through each resistor is the same.

Current

Once again because there is only one path in a series circuit, for the case of resistance this means that each electron will have to go through every resister with in the circuit.

1 2 3 .....TR R R R

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Therefore the total resistance is the sum of all the resistors found in the circuit.

Resistance

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In the picture above, the skate boarder has a drop in gravitational potential energy at each stage during the trip.

This is very similar the drop in electric potential energy (voltage) in a series circuit as an electron passes through a resister.

Potential Difference (Voltage)

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12V

2V 4V 6V

In a series circuit the total voltage drop across the entire circuit is equal to the sum of the individual voltage drops across each resister.

2 4 6 12

1 2 3 .....TV V V V

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Example:What would the potential difference be across the second resister?

4 Volt Drop

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http://www.stmary.ws/highschool/physics/home/animations3/electricity/circuits2_bigger.swf

Find the total current in the circuit below.

Example:

1 2 3 ...TR R R R 2.0 4.0 6.0TR

V IRV

IR

203.3

6I A

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Example:Four loads (3.0 , 5.0 , 7.0 , and 9.0 ) are connected in series to a 12 volt battery.

a) Find the equivalent resistance of the circuit.

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b) Find the total current in the circuit.

0.50 A

c) Find the potential difference across the 7.0 load.

3.5 V

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Parallel Circuit:Circuit in which there are two or more paths for the current to flow.

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Picture walking through a crowded building, and there are that many people that you can hardly move. Then the hallway splits into two hallways of the same size. Half the people go one way and the other go the other way.

Now you have much more room because there are only half as many people in the hallway.

What would happen if the hallway was to split again? And again?

Would you have more and more room to walk each time?

If you have more room would it be easer for you to walk down the hallway? Could you say that there is less resistance to your motion?

Here’s A Thought

This is what happens within a parallel circuit, the more paths that electrons have to chose from, the less over all resistance there is to their motion. 14

In a parallel circuit the total resistance can be found by the following formula

1 2 3

1 1 1 1......

TR R R R

If each resister is 6 Ω, then we get

1 1 1 1

6 6 6TR

1 1

2TR

2R

Because the current had 3 equivalent paths to chose from the over all resistance is 1/3 of what it would have been otherwise.

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Find the total resistance of the given parallel circuit

50Ω

100Ω

250Ω

1 2 3

1 1 1 1......

TR R R R

1 1 1 1

50 100 250TR

1 5 2.5 1

250 250 250TR

25029.411

8.5TR

30TR Not how the total resistance is smaller than any of the individual resistors.

In a parallel circuit the total current is equal to the sum of all of the individual currents through each branch of the circuit

2 A 3 A

3A5 A 17

In a parallel circuit the total current is equal to the sum of all of the individual currents through each branch of the circuit

1 2 3 .....TI I I I

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-12V

12V

12V

12V

In a parallel circuit the total voltage is the same as the voltage across each individual resistor.

1 2 3 .....TV V V V

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Take a 12 volt battery.

Hook up a wire to each terminalMeasure the voltage anywhere between the two wires

What would the voltage be across a resister that was hooker up at any location between the two wires?

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http://www.stmary.ws/highschool/physics/home/animations3/electricity/circuits2_bigger.swf

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Find the total current of the given parallel circuit

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1

100.2

50

VI

R

1 2 3 .....TI I I I

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2

100.25

40

VI

R

33

3

100.5

20

VI

R

0.2 0.25 0.5TI 0.95TI A

10V

20

40

50

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Solve the following circuit.

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1 2 3 20TV V V V volts 1

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204

5

VI A

R

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2

204

5

VI A

R

1 2 3 .....TI I I I

318 4 4 I

3 10I A

33

3

VR

I

3

202

10R

Example:A 60 V battery is connected to four loads (3.0 , 5.0 , 12.0 , and 15.0 ) in parallel.

a) Find the equivalent resistance of the circuit.

1.46

b) Find the total current leaving the battery.

41.0 A

c) Find the current through the 12.0 load.

5 A24

Pg. 719 #’s 27 – 31 (pdf 89)

DO

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Pg. 724 #’s 32 –35 (pdf 89)

Complex Circuit:

A complex circuit is one that has both series and parallel components at the same time.

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10V

17

4

10 10

6

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Despite their name, the method for working with complex circuits is quit easy. We simplify the circuit into a smaller less complicated circuit, one section at a time.

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10V

17

4

10 10

6

13

10V

30

10

20

The first thing we see here is 3 different series circuits (which can be simplify) embedded within the complex circuit.

Now we have a plane parallel

circuit that we can easily work with.

Example:

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Find the equivalent resistance of the circuit below.

Step 1: Combine the 2 resisters that are in parallel.

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1 1 1 2 1

40 40 40 20TR 20TR

Step 2: Combine the 3 resisters that are in series.

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8 20 12 40TR

Step 3: Combine the 2 resisters that are in parallel.

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1 1 1 2 1

40 40 40 20TR 20TR

Step 4: Combine the 2 resisters that are in series.

20 20 40TR

DO

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Pg. 728 #’s 36 & 37 (pdf 89)

Pg. 733 #’s 1-7 (pdf 89)

Do Your Ohm Work

RRHS Handout