Electric Circuits

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El t i Ci itElectric Circuits

Rapid Learning Core Tutorial Series

Rapid Learning Centerwww.RapidLearningCenter.com/© Rapid Learning Inc. All rights reserved.

Wayne Huang, Ph.D.Keith Duda, M.Ed.

Peddi Prasad, Ph.D.Gary Zhou, Ph.D.

Michelle Wedemeyer, Ph.D.Sarah Hedges, Ph.D.



Objectives

Understand and utilize Ohms law

By completing this tutorial, you will:

Ohms law.

Calculate electric power.

Describe the characteristics of series and parallel circuits.

Calculate various electric

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Calculate various electric quantities in circuits.

Learn the basic concepts pertaining to Kirchoff’s laws.

Concept MapPhysics

Studies

Previous content

New content Alternating Current

Electrical Forces

Electric Charge

Direct Current

Described by

or

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Moves in Circuits

Ohm’s Law

Current

Described by

Series Circuit

and

ParallelCircuit



Ohm’s Law

Ohm’s law describes the basic quantities present in any electrical circuit

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present in any electrical circuit.

Basic Electric Circuit

+-

-

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In a circuit, the electrons are flowing or moving. They are not stationary or static.



Sign Conventions

Electrons will obviously move from the negative to the positive terminal of the battery.However, long ago it was thought that positive

+ Conventional current

, g g g pcharge flowed. This convention remains.

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Most of the time the actual direction of flow is very unimportant.

-actual current

Common Schematic Symbols

Conducting Wire: Switch: Light Bulb:

Battery or Voltage Source: AC Voltage: Capacitor:

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A

Ammeter:

V

Voltmeter: Resistor:



CurrentCurrent describes the number of electrons flowing in a circuit.

It’s very analogous to water flowing in a hose orIt s very analogous to water flowing in a hose or pipe.

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It doesn’t count the actual number of electrons, that would be too cumbersome.

Amperes

Current is typically measured in Amperes. (Amps for short or A)

1 Amp = 1 Coulomb / second.

1 Amp is a relatively large amount of current, often

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p y g ,milliamps, mA are used. 1000mA = 1 A



Direct Current

DC, Direct Current: the charge flows in one direction only.

Examples: batteries

Conducting wire-

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Alternating Current

AC, Alternating Current: electrons in the circuit move in one direction, then switch and then flow in the opposite direction.

Conducting wire

-- -- -

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Examples: wall outlets



AC Frequency

Since AC current changes direction, or oscillates, you can describe how often it changes direction.

Almost all US outlets use a frequency of 60 Hz.

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Adapters/TransformersOften it is useful to convert AC into DC, or vice versa.

To save batteries, you’ve probably plugged a radio or CD player into the AC wall outlet with the help of an AC to

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pDC adapter.



Changing Current Types

Diodes allow electrons to flow in one direction only. They help change AC into DC. They are a one way path for electrons.

Notice the input/output voltages, and frequency.

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A diode inside this transformer helps change AC into DC.

Voltage Sources

No current will flow unless there is a voltage source. This is also known as a potential difference.

Sometimes, this potential difference is supplied by batteries!

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Electric Potential Analogy

Imagine a rock laying on level ground. It will not move anywhere (no current) since there is no difference in elevation (voltage).

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Electron FlowHowever, an object at the top of a hill could roll down (current flowing) because of the elevation difference (voltage).

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Shocking Experience

To receive a shock, there must be a voltage difference applied to you. (electrons must “roll” downhill)

This is often referred to as an electric potential difference.

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A Bird on a WireA bird could sit on a high voltage wire and receive no shock at all. Its entire body is at the same high voltage. No voltage difference.

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However, if it touches the ground, tower, or wire with a different voltage then there would be a large voltage difference, and the current would flow!!!



Grounding

To prevent electric shock, most cords have a third prong that is used to ground the cord.

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If there are any extra electrons, they are immediately sent to the ground, not you.

Electrical Resistance

In almost all circuits, the electrons flow with some opposition or resistance.

Resistance is measured in units called Ohms.

The symbol is the Greek letter omega: Ω

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Resistors on a circuit board



Analogy

A hose is like wire

A pump is like voltage

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As mentioned earlier, there are many similarities between electrical circuits, and “water” circuits.

A valve is like a switch

Ohm’s Law

Mr. Ohm discovered an extremely useful relationship: Voltage = Current x Resistance

IRV =Voltage, V

Resistance, Ω

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Current, Amperes, A



Ohm’s Law ExampleA light bulb operates on a 110 volt circuit. The bulb draws a current of .91 amps. What is the resistance of the light bulb?

V = IRR = V/IR = 110V/.91AI = 120.8 Ohms, Ω

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Internal Resistance

You may measure the potential difference of a battery at 9V:

9V

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9 V



Voltage Difference

However, if you insert that battery into a circuit, measure its voltage again, you may find its somewhat lower!?!

8.5V

8.5 V

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Internal Resistance DiagramThis difference is due to the internal resistance of the battery itself.

+-

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Once the battery is hooked into a circuit, there is current flowing.

battery

When this current encounters even minor resistance in the battery, there is some voltage drop when compared to earlier.



EMF

When in a circuit, the reduced voltage is referred to as the terminal voltage.

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The potential difference when nothing is connected is referred to as the EMF, electromotive force. This term has nothing to do with the traditional notion of force.

Lost Voltage

When you take away the voltage lost due to the internal resistance from the EMF, the remaining voltage is the terminal voltage:

EMF - IRbattery = Vterminal

voltage is the terminal voltage:

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EMF - “lost voltage” = terminal voltage



Energy Conservation

Energy, or voltage, is still conserved. Some is simply used up by the internal resistance of the battery itself.

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The actual internal resistance of most batteries is very small, less than 1 Ohm.

Internal Resistance Example

As in the previous discussion, the 9 V battery has a terminal voltage of 8.5 V when connected to a 100 Ω resistor. What is the internal resistance of the battery?

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?



Internal Resistance Solution

First, it may be useful to find the current:

.085A8.5VVI ===

Then, use the idea of internal resistance:

EMF - IRbattery = Vterminal

.085A100ΩR

I

8 5Vr085A9V

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8.5Vr.085A 9V battery =−

5.88Ωr battery =

.5Vr.085A battery −=−

Electric Power

Just as power was used to discuss mechanical work per unit of time

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mechanical work per unit of time, electrical power works the same way.



Electric Power

Just like mechanical power, electrical power describes work done per unit of time.

1 Watt = 1 Joule / 1 second

1000 Watts = 1 kilowatt

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Power Formula

In terms of electrical quantities, power can be calculated by multiplying current x voltage.

IVP =

Electric Potential, V

Electric Power

Watts, W.

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Current, Amperes, A



Alternate Power Formula

Another formula for power can be found.

Since V = IR

And P = IV

Substitute V into the power equation and obtain:

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P = I2R

Power ProblemHow much current flows through a 100W light bulb if its connected to a 120V fixture?

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Example SolutionThe bulb is 100 W when it has a potential difference of 120 V applied.

P = IVI = P/VI = 100W/120VI = 0.83 Amps

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Electric Bill

Look at an electric bill.

You’ll notice that you pay $ for every kilowatt-hour used.kilowatt hour used.

( ~ $.10 per kW hr )

Thus, for every hour you use 1000 Watts, you would pay $ 0.10.

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A kilowatt-hour is a unit of energy, not power.



Another Power ProblemMaybe your parents are always telling you to turn off the lights and save electricity/money? How much would it cost to run a 100 W bulb for 4 hours if it were connected to a 120 V fixture? ($0 10 perif it were connected to a 120 V fixture? ($0.10 per kW hr)

100 W = .1 kW

0.1 kW x 4 hrs = 0.4 kW hrs

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0.4 kW hrs x $0.10 = $0.04!

Series and Parallel Circuits

Electrical components can be connected in various ways This drastically changes

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in various ways. This drastically changes the properties of the circuit.



Series Circuits

One simple way to arrange components in an electrical circuit is to create one large continuous loop with the components:loop with the components:

Two Batteries

Switch

Light Bulb

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Bulb

Resistor

This is similar to a TV series where one episode follows another.

Series Circuit Characteristics

1. The current is constant throughout the circuit.

f2. Individual components may use varying amounts of voltage.

3. The total voltage use is equal to the voltage of the battery/power supply.

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4. A break in the circuit interrupts the entire circuit.



Adding Resistors in Series

When resistors are added in series, the total resistance of the circuit is the sum of those individual resistors.

...RRRR 321S ++=

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Series or total

combined resistance, Ω

Individual resistors, Ω

Parallel Circuits

Another way to connect a circuit is in parallel. In this arrangement, each component is connected separately in its own “loop”.

Two Batteries

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Three Resistors in Parallel



Parallel Circuit Characteristics

1. The current in the different branches can vary.

f f2. The total current of the circuit is the sum of the individual branches.

3. All branches of the circuit receive the same voltage of the battery/power supply.

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4. A break in one loop doesn’t affect the others.

Resistors in Parallel

To find the equivalent resistance of resistors added in parallel:

...R1

R1

R1

R1

321P

++=

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Parallel or total combined

resistance, ΩIndividual

resistors, Ω



Parallel Resistor ExampleCalculate the total effective resistance of two 10 Ohm resistors connected in parallel.

111+

21P RRR+=

10Ω1

10Ω1

R1

P

+=

21

Combine, use common

denominator if needed

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10Ω2

R1

P

=

5ΩRP =

Take the reciprocal of each side of

equation

Parallel Resistor Observations

5 Ohms. Notice that the total overall resistance is lower than either one of them individually!

This occurs because there are multiple paths for the electrons to take, lowering their resistance.

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Too Many Resistors

Adding more and more devices in paralleldevices in parallel decreases the total or overall resistance. This allows too much current to flow! Obviously this can be dangerous!

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Combination Question

Often, when one Christmas tree light goes out, they all go out!!! How are these type of lights wired together?

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These are wired in series. A parallel arrangement would eliminate this…



Fuses and Circuit Breakers

To prevent too much current from causing a fire, fuses are designed to melt and break the circuit before that happens.

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Today, most homes have circuit breakers. These don’t melt, but are switched off to interrupt the circuit.

MetersMetersA multimeter can measure voltage, current and resistance.

Meters can provide either digital or analogreadouts.

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Digital Analog



Measuring Current

Current can be measured using an ammeter or a multimeter.

A meter that only measures current iscalled an ammeter.

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Using Meters to Measure Current:

When measuring current, the meter leads are connected in-line with the load or voltage source.

A

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Connecting a Meter for Current

Notice that the meter leads or probes are placed in line with the load. This is called a series

ti

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connection.

Using Meters to Measure Voltage

When measuring voltage, the meter leads (probes) are placed across the load or voltage source

V

source.

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Connecting a Meter for Voltage

Notice that the meter leads or probes are placed across the load. This is called a parallel connection.

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Circuit Problems

This section will detail how to calculate the various electrical quantities in a

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the various electrical quantities in a circuit.



Series Circuit

Calculate the current and electric potential difference for each component of the circuit shown.

R2=

10Ω

5V

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R1 = 5Ω

A good first step is to simplify the circuit.

Circuit SimplificationBecause this is a series circuit, to combine the resistors and simplify the circuit, they are merely added together.

R2=

10Ω

5V 5V

Rs=

15Ω

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R1=5Ω...RRRR 321S ++=

15Ω10Ω5ΩRS =+=



Current in a Series Circuit

5V =15Ω

IRV =VI =5V

Rs=

Use the voltage of the power supply and the total resistance of the circuit to find the total current

R.33A

15Ω5VI ==

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flowing through the circuit.

Because the electron flow has no where else to go, this amount is also the current flowing through both resistors. I1 and I2 is that same .33 Amperes.

Voltage in a Series Circuit

10Ω

5V

Since we know the current flowing through each resistor, we can use Ohm’s

R2=

R1=5Ω

5Vlaw to find the potential difference for each of those resistors.

IRV1= IRV2=

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) (.33A)(5ΩV1=

1.67VV1 =Notice how the sum of the two voltages adds up to the power supply for the circuit.

) (.33A)(10ΩV2=3.33VV2 =



Parallel Circuit

Calculate the current and electric potential difference for each component of the circuit shown.

5V

R1=5Ω R2=10Ω

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Notice how this parallel circuit contains the exact same components as the series circuit, they are just arranged differently.

Again, a good first step is to simplify the circuit.

Circuit Simplification

5V

21P R1

R1

R1

+=

R1=5Ω R2=10Ω

11110Ω

3R1

P

=

10

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10Ω5ΩRP

+=

10Ω1

10Ω2

R1

P

+=

3.3ΩΩ3

10RP ==

Notice this parallel resistance is less than either one individually.



Shortcut Formula

An equivalent formula can be used for tworesistors, R1 and R2, connected in parallel. Sometimes this formula is easier to manipulate.

21

21P RR

RRR+

=

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It may be easier to remember this formula as the product over the sum for the two resistors.

Voltage in a Parallel Circuit

5V

R1=5Ω R2=10Ω

The easy part about any parallel circuit is the voltage applied to each item.

Si h it h it i d d t

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Since each item has its own independent connection to the battery or power supply, each item receives that voltage.

In this case, V1 and V2 are each 5V.



Current in a Parallel Circuit

5V

R1=5Ω R2=10Ω

Once you realize that the electric potential for each resistor is 5V, finding the current is easy using Ohm’s law, V=IR.

V 2VI

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1

11 R

VI =2

22 R

VI =

1A5Ω5VI1 == .5A

10Ω5VI2 ==

Current Observations

5V

R1=5Ω R2=10Ω

Notice the two currents add up to the same value as the total current in the circuit. This is a good way to check your work.

5VV

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1.5A3.3Ω5V

RV

IT

T ===

1.5A.5A1AIII 21T =+=+=



Kirchhoff’s Laws

Kirchhoff’s laws describe more complex circuits The concept is relatively simple

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circuits. The concept is relatively simple, but the application to a circuit can be a bit complex.

Multiple Voltage Sources

Typically, Kirchhoff’s laws are used when there are multiple voltage sources and/or loops in the circuit.

+ _

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The multiple voltage sources may even “oppose” each other.



Junction Rule

The current going into a junction (intersection) is equal to the current leaving the junction.

8 A

4 A4 A

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This junction rule can be considered a restatement of conservation of charge.

4 A4 A Conducting wire

Loop RuleThe sum of the voltage changes for all elements in a loop must equal zero.

VR

esis

tor

1V

4V

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The loop rule can be considered a restatement of conservation of energy.

03V1V4V =−−+Resistor 3V



Using the Loop Rule

• Guess (educated?) at a direction of conventional current flow. Draw it into your diagram.

• Label ends of battery. Long end +.

current flow. Draw it into your diagram.

• Resistor voltage is – if you move in the same direction as the current.

• Battery voltage is + if you go from the negative to positive battery terminal.

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• Finally, create an equation using the loop rule and the path of the current.

• If the current is - , your original direction was wrong.

p y

Example

+ _10V 5 Ω

Current Ohm units have been

+_

6V10 Ω

guess

05I10V10I6V =−−−−IRV =

have been omitted for clarity Starting

point

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05I10V10I6V =015I16V- =−

1.07A15Ω16VI −=

−+

=Current goes opposite direction



Multiple Loops

When there are multiple loops, both the loop and junction rule may be required.

You may have multiple unknowns.

You must have as many equations as unknowns in order to solve.

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Once one variable is found, substitute it to find the others.

Kirchhoff’s Laws ExampleI1

I2

312 III +=22 Ω+ _

9V

I2

I3 6V

15 Ω

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09V22I-15I 12 =+−Top loop:

Bottom loop: 015I6V 2 =−−

6V



Problem Solving - 2Work with the bottom loop first since its simplest:

Amps156I2 −=015I6V 2 =−− 15

Thus, our original guess for the direction of I2 was wrong!

Put I2 back in and find I1.

09V22I-15I 12 =+−

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12

09V22I- 15(-.4) 1 =+−

0922I6 1 =+− .68AI1 =

Problem Solving - 3With our revised current direction, we now know I1 and I2.

22 Ω+ _I1

6V

15 Ω

I2

I3

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.4A +.68A = 1.08A in the opposite direction to what we originally thought.

I3

We can finally get I3:



Parallel connections have

Parallel connections have

Current is charge per unit of time

Current is charge per unit of time

Kirchhoff’s loop and junction rule Kirchhoff’s loop and junction rule

Learning Summary

Series connectionsSeries connections

connections have separate loops.

1/RP=1/R1+1/R2+…

connections have separate loops.

1/RP=1/R1+1/R2+…

unit of time. 1Ampere =

1C/1s

unit of time. 1Ampere =

1C/1s

jdescribe more

complex circuits.

jdescribe more

complex circuits.

Ohm’s law:Ohm’s law:

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Series connections are in one

continuous loop.Rs = R1+R2+R3…

Series connections are in one

continuous loop.Rs = R1+R2+R3…

Ohm s law:V = IR

Power formula:P = IV = I2R

Ohm s law:V = IR

Power formula:P = IV = I2R

Congratulations

You have successfully completed the tutorial

Electric Circuits

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Electric Circuits

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