© 2001-2005 shannon w. helzer. all rights reserved. unit 12 electricity and rc circuits

© 2001-2005 Shannon W. Helzer. All Rights Reserved.

Unit 12Electricity and RC Circuits


Conduction ElectronsIn organic compounds, electrons are bound to specific atoms.In metallic compounds, some of the electrons are not bound to a specific atom.They are free to move throughout the metal.These electrons are called conduction electrons.If a potential difference is placed across the wire (like when you connect the wire to a battery), then the electrons will move.As they move, the electrons collide with the metallic atoms.Depending upon the number of collisions an electron has, it may move faster or slower through the metallic structure.Remember, moving electrons in a wire are known as current.

12-1


Batteries

Batteries come in many shapes and sizes that have a variety of voltage and currents.Identify the voltages of the four common battery types shown below.

12-1A


BatteriesThis slide will explain how a battery provides electricity for use in your small electrical appliances.Free electrons and “holes,” which are the absences of electrons, are produced within the battery due to electrochemical reactions.

12-2


CapacitorsLike batteries, capacitors come in a wide assortment of shapes.A capacitor acts as a buffer to temporally store excess charges.At other times a capacitor acts as a short lived battery in order to provide additional current (electrons) when the need is larger than a battery can provide.Basically, a capacitor consists of two parallel plates.One of these has a net positive charge while the other has a net negative charge.In the next slide we will take a closer look at the operation of a capacitor.

12-3


CapacitorsObserve the capacitor acting in the capacity of a short lived battery.

12-4


Resistors

Resistors impede the flow of electrons (current).They impede this flow because certain electrical items have maximum limitations on the current they can handle.Consider the Light Emitting Diode (LED) in the figure to the right.The battery supplies too high a current to the LED.As a result, the LED is damaged by the current.When a resistor is placed into the circuit, the current is reduced to a level appropriate for use with the LED, and the LED is not damaged.

12-5


Batteries and CurrentA complete circuit is one that connects a battery to an electrical component back to a battery.Remember, current flows from the negative end of a battery through the light bulb (resistor) and back into the positive end of the battery.The symbol “I” is used to denote current.Current is the number of electrons passing a certain point in a circuit per unit of time.We draw an arrow in the direction that the current would flow through the circuit.

12-6


Multiple Batteries and CurrentDepending on how they are placed, multiple batteries in a circuit can enhance or impede the current in a circuit.Consider the circuit below. The current flowing through both batteries travels in the same direction.As a result, the net current is enhanced in the circuit.Now, let us flip one of the batteries.When we flip the battery, its current now acts in the opposite direction.As a result, it impedes the current.Since both batteries are the same, no net current flows, and the bulb goes out.

12-7

1I 2I


Multiple Batteries and CurrentIn this figure the batteries are of different voltagesAs in the previous figure, when the batteries are connected in the same way, the net current is enhanced.When one battery is flipped, the net current is impeded.Determine the net current direction and the net voltage of the circuit below.The key to determining the net current direction lies in considering the voltages of the batteries.The net current will flow in the direction of the current belonging to the battery with the highest voltage.

12-81I

2I


WS ???? #2

Determine the voltage and the net current direction in the circuits below.

12-9

+-

6 Volt

+ -

6 Volt

+-

6 Volt

+ -

6 Volt


Circuit Configurations: Series Resistors

Look at the drawing animation below.The skateboarders leaving the school only have one place to go.They also only have one place to return to.Their round trip occurs in a series circuit.

12-10


Circuit Configurations: Series ResistorsNow lets replace the school building with a battery.Turn the house and restaurant into a light bulb (resistor).Change the roads into wires.Now let some electrons flow through the circuit.They have only one destination: through the resistor and back the battery.

12-11


Circuit Configurations: Multiple Series ResistorsThe lights below are in series with each other because the same current flows through all three of them.Notice how the first bulb is brighter than each consecutive bulb thereafter.This is because the electric potential (voltage) drops as it passes through the resistor.As a result, there is less voltage available for the next resistor.

12-12

1I


Circuit Configurations: Parallel Resistors

In a parallel circuit, the skateboarders have a choice of going home or to the Big Burger for lunch.They make this choice at the intersection.When there is an intersection resulting in a choice between two or more directions, the circuit is a parallel circuit.

12-13


Circuit Configurations: Parallel ResistorsNow let us make the appropriate replacements in this circuit and turn it into an electrical circuit.Now allow the current to flow.Notice how more electrons flow through the small bulb.This action happens because the small bulb has a lower resistance than the large bulb.We will look at resistance more in the next slide.

12-14


ResistanceLets consider the circuit to now have two ramps.Most unskilled skateboarders would choose the lower ramp.As a result, we could say that the lower ramp has a lower resistance.Now let us make the appropriate replacements.In this replacement, we replaced the ramps with actual resistors instead of with light bulbs.As you can see, more electrons flow through the orange resistor because it has a lower resistance.

12-15


+-

Circuit Configurations: Multiple Parallel ResistorsThe circuit to the right shows three parallel resistors (bulbs) that are in series with a fourth resistor.When we close the top switch, the two lighted bulbs are in series, and the top bulb is slightly brighter than the bottom bulb.They share equal currents.What do you think will happen when we close the middle switch?Notice that the top two bulbs were equally dimmed while the bottom bulb remained the same.The currents through the top bulbs are equal but half that through the bottom bulb.A similar result is observed when the bottom switch is closed.

12-16

1I


A Closer Look – Series ResistorsWhen the switch to the right is closed, which bulb will be brighter?Why?The voltage drops across R1 making R2 less bright than R1.If we remove R2, then what will happen to R1?Why? The same current flows through both light bulbs (resistors).If you remove one of these series resistors, then the current can not flow, and the bulbs go out.

12-17

+-

R1

R2


A Closer Look – Parallel Resistors

Note: R2 = 2.0 and R1 = 1.0 When the switch to the right is closed, which bulb will be brighter?Why?R1 will be brighter because more current will flow through it due to the fact that it has less resistance.If we remove R1, then what will happen to R2?Why? R2 will get brighter because all of the current now passes through R2 instead of being split between R1 and R2.

12-18

+-

6 Volt

R1

R2


A Closer Look – Combination ResistorsNote: R4 = 4.0 , R3 = 3.0 , R2 = 2.0 , and R1= 1.0 .When the switch to the right is closed, which bulb will be brighter? Why?All of the current flows through R1 before it splits after R1.What will happen to R4 if we remove R1?Why?All of the bulbs go out because the electrons can not flow through R1.What would happen to R1, R3, and R4 if we removed R2?Why?What would happen to R2 and R1 if we removed R4?Why?

12-19

+-

R1

R2 R3

R4


Schematic SymbolsWhen engineers design electrical circuits, they replace actual pictures of electrical components with schematic symbols.Here are five electrical components we will use frequently.The schematic symbol for each of these electrical components is as follows.Here are some other symbols you must be familiar with.

12-20

V

A


Parallel and Series Electrical ConfigurationsThere are two basic electrical configurations: series and parallel.In a series connection, all electrical components share the same current.In a parallel connection, the current through each component varies depending upon the components resistance.Let us take a look at the schematic diagrams for the circuits below.In the lower left picture, the two resistors are series.Note that we can move one of the resistors any where in the circuit while maintaining the same current through each.In the lower right picture the resistors are parallel.Again, we may move one resistor and still have a parallel circuit.The resistors do not need to be geometrically parallel in order to be electrically parallel.

12-21


Equivalent CircuitsIt is often desirable to reduce numerous electrical resistors in a circuit to an equivalent circuit with fewer resistors.In a series circuit, the series resistors may be replaced with a single resistor with the equivalent resistance to that of the ones it replaced.On paper, simply redraw the circuit with only one resistor in the place of the two (or more) you are replacing.The same concept holds true for parallel resistors.The exact same procedure is followed when doing equivalent circuits with capacitors instead of resistors.

12-22

1R 2ReqR 1R

2R

eqR


Series TestSeries Component Test – must be able to go from only one side of a component to only one side of an equivalent component without passing an intersection or a nonequivalent component.An intersection kills a series possibility.Are R4 and R2 Series?Are R5 and R3 Series?Are R4 and R5 Series? Are C2 and C1 Series? Are C3 and C4 Series?

12-23

R3

R1 R2

C2

C1

R4

C4

C3

R5


Parallel TestParallel Component Test – must be able to go from both sides of a component to both sides of an equivalent component without passing through a nonequivalent component.An intersection has no impact on a parallel circuit possibility.Are R3 and R1 Parallel?Are R4 and R2 Parallel? Are C2 and C1 Parallel?

12-24

R3

R1

R2

C2

C1

R4

C3


Series & Parallel TestThe circuit to the right is a very complicated RC (Resistor-Capacitor) circuit.Let us apply the tests for series and parallel circuits in order to reduce the circuit to its simplest form.Always replace series components with their equivalent series component before attempting to replace parallel components.Do you see any series components?Once all series components are replaced, proceed to replace any parallel components that may remain.Are the remaining resistors series?Why or why not?Once there are no longer any series or parallel components, the circuit is reduced as far as possible.

12-25


Equivalent Resistance for Series CircuitsWhen you replace series resistors with an equivalent resistance, you must calculate the value of the new resistor.When replacing two series resistors with an equivalent resistance, use the following formula in calculating the equivalent resistance.

If you are replacing many resistors, use the following formula in order to calculate the equivalent resistance.

12-26

21 RRReq

...21 RRReq1R 2ReqR


Equivalent Resistance for Parallel CircuitsWhen you replace parallel resistors with an equivalent resistance, you must calculate the value of the new resistor.When replacing two parallel resistors with an equivalent resistance, use the following formula in calculating the equivalent resistance.

If you are replacing many resistors, use the following formula in order to calculate the equivalent resistance.

12-27

21

111

RRReq

...111

21

RRReq

1R

2ReqR


1C 2CeqC

When you replace series capacitors with an equivalent capacitance, you must calculate the value of the new capacitor.When replacing two series capacitors with an equivalent capacitance, use the following formula in calculating the equivalent capacitance.

If you are replacing many capacitors, use the following formula in order to calculate the equivalent capacitance.

Equivalent Capacitance for Series Circuits

12-28

21

111

CCCeq

...111

21

CCCeq


eqC

Equivalent Capacitance for Parallel CircuitsWhen you replace parallel capacitors with an equivalent capacitance, you must calculate the value of the new capacitor.When replacing two parallel capacitors with an equivalent capacitance, use the following formula in calculating the equivalent capacitance.

If you are replacing many capacitors, use the following formula in order to calculate the equivalent capacitance.

12-29

21 CCCeq

...21 CCCeq

1C

2C


WS ??? # 1 and WS ??? #1Find the equivalent capacitance or resistance for the circuits in the following problems.WS ??? # 1. If C1 = 5.0 F, C2 = 25.0 F, and C3 = 9.5 F, then Ceq = ____?WS ??? # 1. If R1 = 5.0 , R2 = 25.0 , and R3 = 9.5 , then Req = ____?

12-30

R1

R2

R3

C1

C2

C3

21 CCCeq 21

111

CCCeq

21

111

RRReq

21 RRReq


WS ??? # 1 and WS ??? #1Find the equivalent capacitance or resistance for the circuits in the following problems.WS ??? # 1. If C1 = 5.0 F, C2 = 25.0 F, and C3 = 9.5 F, then Ceq = ____?WS ??? # 1. If R1 = 5.0 , R2 = 25.0 , and R3 = 9.5 , then Req = ____?

12-31

21 CCCeq

21

111

CCCeq

21

111

RRReq

21 RRReq C3

C2

C1

R1

R2

R2


WS ??? # 4Find the equivalent capacitance or resistance for the circuits in the following problems.If R1 = 5.0 , R2 = 25.0 , and R3 = 9.5 , then Req = ____?

12-32

21 CCCeq

21

111

CCCeq

21

111

RRReq

21 RRReq

R1

R2

R3

R1 R2


WS ??? # 4Find the equivalent capacitance or resistance for the circuits in the following problems.If C1 = 12.0 F, C2 = 25.0 F, C3 = 5.0 F, and C4 = 1.5 F, then Ceq = ____?

12-33

C3

C2

C1

C4

C421 CCCeq

21

111

CCCeq

21

111

RRReq

21 RRReq


Resistor/Capacitor Circuits WS ??? # 2Reduce the circuit below as far as possible by finding the equivalent capacitance and resistance. Draw the final circuit for each problem. C1 = 22.8 F, C2 = 2.3 F, C3 = 5.9 F, C4 = 5.0 F, R1 = 2.2 , R2 = 14.8 , R3 = 9.5 , and R4 = 12.0 .

21 CCCeq

21

111

CCCeq

21

111

RRReq

21 RRReq

R2 R3

R1

C3

C2

C1

12-34


Ohm’s LawOhm’s Law gives us a mathematical expression relating the voltage (V), Current (I), and Equivalent Resistance (R) of a circuit.

Previously, we reduced the circuit below to its equivalent resistance.If we do not know the voltage but we do know the current and the resistance, then we can use the equation to find the voltage.

If we know the voltage of the battery and the resistance, then we can find the current flowing through the resistor.

12-35

eR qV I

1R

2ReqReR q

VI

eR qV I


Ohm’s LawYou can use Ohm’s Law to calculate the current through a resistor if you know the voltage across the resistor and the resistance of the resistor.Consider the parallel circuit below.Suppose the voltage (V) of the battery in both circuits below is 10.0 V.Since both sides of the battery are connected to both sides of both resistors, the voltage across both resistors would be 10 volts.However, they would not have the same current because the current splits before it reaches the resistors.You can use Ohm’s law in order to find the current through these resistors.

12-36

1R

2R

V

11R

VI 2

2R

VI

1I

2I

1I

2I

I

1 2I I I

I


Ohm’s LawBoth sides of the resistors below are not connected to both sides of the battery.As a result, they do not have the same voltage across them.However, as these resistors are in series, they share the same current.The voltage drop across R1 (from A to B) is given by the equation below right (Ohm’s Law).The voltage would also drop across R2 and can be calculated with the equation below left.

12-37

1R2R

V I

2RB CV I ABC

1RA BV I


Ohm’s Law Example 1

R1 = 10.0 , R2 = 20.0 , and R3 = 30 .What is the current through the circuit below?What are the voltage drops through R1, R2, and R3?

12-38

1IR1

R2 R3


+-

Ohm’s Law Example 2R1 = 10.0 , R2 = 20.0 , and R3 = 30 .What is the current through each resistor in the circuit below?What are the voltage drops through R1, R2, and R3?

12-39

R1

R2

R3


Power Once we know both the current and the voltage across a resistor, we can

determine the power consumed by that resistor. The power consumed may be determined using the following equation.

The power consumed in R1 in both circuits below may be determined as follows.

1R2R

V I

ABC

1RA BV I

1 A BP V I

P VI

1R

2R

V

1I

2I

1I

2I

II

11R

VI

1 1P VI

11

VP V

R

2

11

VP

R

1 1P IR I2

1 1P I R

12-40


Batteries and emfSo far we have considered batteries as perfect sources of electrons meaning that all the electrons produced by the electrochemical reactions inside the battery are delivered to the electrical circuit.However, this statement is not true because of the fact that the materials the battery is made of resist the flow of electrons produced by the battery itself.We call this resistance the internal resistance (r) of the battery.This internal resistance, when multiplied by the current flowing through the battery, reduces the electric potential (voltage) the battery can deliver to the circuit.Consider the D-Cell battery below that provides a voltage (V) of 1.5 V to a circuit.The actual electrical potential produced by the battery known as the electromotive force (emf or ) is larger than the voltage V delivered.The relationship between the emf and the battery voltage is given in the below equation where I is the current produced by the battery.The schematic symbols for a battery with and without internal resistance is given below.

12-41

V VrV Ir


Electro Motive Force (emf)The V below is the ideal value of the voltage across the battery (i.e. 9 Volts).

Although the potential difference across the terminals of a battery is V when no current is flowing, the actual potential difference is reduced when a current is flowing through the battery due to internal resistance (r)in the battery.The actual potential difference is known as the electromotive force, .When we consider the internal battery resistance, the figure below would change to look as follows.The electromotive force may be found by using the following equation.

The internal battery resistance is treated like a regular resistor, R, when doing calculations.

12-42

BA

V

R

BA

R

r

IRIrVab

IRVab


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© 2001-2005 shannon w. helzer. all rights reserved. unit 12 electricity and rc circuits

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