Electric Current• Electric current is the flow of charged

particles.• In its most common, everyday form,

current is a flow of electrons in a wire. We can harness the energy of these moving electrons and make it do work for us (i.e., lighting a bulb, turning a motor, warming a heating element).

• In order for charge to flow as a current it is essential that you have a steady potential difference (voltage) between the source of the charges and the destination.

What do we do with current?

1) Light2) Heat3) Motion (Kinetic Energy)4) Digital Computing*

*This last category is not so much a transfer of energy like the top 3, but rather the re-routing of electrons in a logic circuit to produce predefined outcomes

Electric Circuits• Although we now know that the negative

charge carriers (the electrons) are the thing actually moving in a conductive, electrical wire, this was not understood when electricity was first discovered.

• Because many of the relationships between components in an electric circuit had been formalized before we (humanity) learned about the atom, by convention we describe current as the flow of positive charge!

Current and Circuits (cont’d)• In order to move charge from any point A, to any

other point B, we have already stated that a potential difference is needed between the points. This usually takes the form of some sort of “charge pump” like a generator or a battery.

• In order for charge to move, we also need a material that allows the individual charges to move easily through it (a conductor)

• As the word “circuit” implies, in order to have current flow, we generally need a closed loop or circle of conductive material that connects charge pump (point A) to electrical user (point B) and back to the pump. The reason for this is that the pump usually serves as source and sink of extra charge.

Ben Franklin’s “Mistake”

Which is correct?BOTH!

• As long as notation is consistent, a “forward” flow of protons is physically and mathematically the same as a “backward” flow of electrons.

• We will utilize the direction of conventional current for all analysis in this class.

CurrentCurrent is defined as the rate at which charge flows

through a surface.

The current is in the same direction as the flow of positive charge (for this course)

Note: The “I” standsfor intensity

AmpAmpereqt

dq

t

qI

seconds

Coulombs

Current: The Details

• Current: Moving charge of any type, technically the rate of charge vs. time

• Variable: I or i (depends on context)

• Unit: Ampere, or Amps– Abbreviation: A– Current is measured as a rate (like velocity)

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C1A1

Why does current flow?• Charge will move as current if it is

provided with a large enough potential to do so (i.e., voltage), that is to say a Coulombic force pushes it.

• Recall that the work done to a falling body is the same as the potential energy from the height at which it fell from. You might say that a rock dropped from a height has the potential to fall and gain speed.

There are 2 types of CurrentDC = Direct Current - current flows in one direction

Example: Battery

AC = Alternating Current- current reverses direction many times per second. This suggests that AC devices turn OFF andON. Example: Wall outlet (progress energy)

• You can think about voltage (potential difference) the same way. If you put an electron near a whole bunch of other electrons there is a high potential energy since it is extremely likely that the single electron will get repelled by the group, right?

• So, for a single charged particle

Voltage = W / q = PE / q

Potential Difference =Voltage=EMFIn a battery, a series of chemical

reactions occur in which electrons are transferred from one terminal to another. There is a potential difference (voltage) between these poles.

The maximum potential difference a power source can have is called the electromotive force or (EMF), . The term isn't actually a force, simply the amount of energy per charge (J/C or V)

Other Variables: Power• As current flows through an electric circuit

and encounters some object that harnesses some of this moving electrical kinetic energy to do work (let’s say a motor: the electricity causes something to move), as in most natural processes it is impossible to transfer all the electrical energy to kinetic energy in the motor. Waste heat is always generated as well.

Power (cont’d)

• Not all the electrical energy is used by the motor and/or converted to heat. The excess current returns to the charge pump and is cycled again.

• Recall that P = W / t

• The power dissipated by a circuit is simply the current flow multiplied by the voltage across the pump.

2P IV=I RWhat is a Watt? Do the units of power work out to be Watts?

Resistance• You may think of resistance as simply being

friction caused by electrons rubbing inside a wire, but it is much more than that.

• Any object or device that uses current to perform work, like a light bulb or motor, does so by “grabbing” moving electrons as they flow by. The more e-’s the device grabs, the larger the resistance of that device to current flow.– What are some examples of useful resistors?

• There are devices simply called “resistors” that we often put into an electric circuit to reduce the voltage or the “load” on a device in the circuit.– Where do you think we might use these?

MORE LATER!!!

Factors affecting resistance

• Like friction affecting the flow of water in a pipe, several factors affect the flow of charge in a wire. They include:– The cross-sectional area of the wire.– The material the wire is made from (this

determines its “resistivity”– The length of the wire.

Resistance: Ohm’s Law

• German physicist Georg Ohm learned via experimentation that the total resistance in an electric circuit was simply the ratio of available voltage to the current flowing in that circuit.

• This is sometimes written as R = V / I, but more commonly seen written as

V = IR

Ohm’s Law“The voltage (potential difference, emf) is directly

related to the current, when the resistance is constant”

IR

IRV

R

R

IV

Resistance

alityproportion ofconstant

Voltage vs. Current

0

1

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1

Current(Amps)

Vo

ltag

e(V

)

Voltage(V)

Since R=V/I, the resistance is the SLOPE of a V vs. I graph

R= resista

nce = slo

pe

Remember doing this lab in Physics 1?

ResistanceResistance (R) – is defined as the restriction of electron

flow. It is due to interactions that occur at the atomic scale. For example, as electron move through a conductor they are attracted to the protons on the nucleus of the conductor itself. This attraction doesn’t stop the electrons, just slow them down a bit and cause the system to waste energy.

The unit for resistance is the OHM,

Units

• In honor of our friend Georg, the SI unit of resistance is called the Ohm designated by the Greek letter omega ().

• 1 Ohm is the resistance that will allow 1 Amp of current to flow when a voltage of 1 Volt is applied to a circuit.

Practice! Arriba!1) Find the potential difference across a

circuit when 0.24 A are applied to a 500 refrigerator.

2) Calculate the resistance of a single light bulb in circuit where a 6 V battery provides 0.045A of current.

3) Find the power dissipated by the bulb in number 2.

Measuring Voltage and Current• Voltmeters: Measure potential difference.

Voltmeters must always be placed in parallel with the device across which they are measuring voltage.– An ideal voltmeter carries _____________

resistance.

• Ammeters: Measure current flow. Ammeter is placed in series with a resistor.– An ideal ammeter carries ______________

resistance.

Series and Parallel

Series

Parallel

Notice ammeter is series with resistors while voltmeter measures the potential drop across RA. Why?

Circuit Schematics

• The following topics mainly involve applications of electric current. The two topic covered are electric energy transfer and transmission of electric power. Please pay close attention, but realize that these are two separate and quick topics.

Electric Energy in Circuits• Recall P=IV and that V=IR, substituting IR

into the power equation the result isP = I2R

• Remember that power is work over time and that work is energy used in a process. If we multiply both side of the equation above, it solves for energy giving us:

E = Pt = I2Rt

• Basically this formula gives us the energy used over a time period by a circuit.

More Practice:• A 15 electric heater operates on a 120

V outlet.a) What is the current through the heater?b) What is the electric power dissipated by the

heating element?c) How much energy is used by the heater in

30.0s?d) How much thermal energy is liberated in this

time?e) Describe another possible approach to this

problem.

Transmission of Power

• Electric power is transmitted directly from an electric generator to the user. Even good conductors induce a small amount of electrical friction or resistance to current flow. From Ohm’s Law recall that a specific length of wire (like from the plant to your house) the resistance is

I

VR

• As the length of the wire increases the resistance increases. In order to get the same amount of current (or any current over very long distances for that matter) the potential difference between the generator and ground (remember the current flows to ground after going though your appliances) must be made larger.

• It seems logical to ask why not just increase the current flow from the source?

• Recall that P = IV = I2R. We get the same increase in power transmission by simply increasing voltage as we do by increasing current. This has 2 advantages:– It is cheaper and easier to raise the potential

difference at the source than to increase the current.

– As current increases, power and heat dissipated increase. If current gets very large the power and heat energy generated increases as I2. Can anyone say melting power lines? I knew you could…

The kilowatt-hour

• Everyone calls them “power companies,” but they are really selling energy.

• Recall that E = Pt =I2Rt

• A simple analysis of the units leaves us with Watts x Seconds. For lots of Watts and lots of seconds together we get the unit kWh.

• Detailed analysis of calculating the cost of electricity can be found in this document

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JJ

Circuit Analysis

Series

Parallel

• When analyzing a circuit we have several tools at our disposal. Ohm’s Law is one of these, but it comes with a few cautions:– When dealing with multiple resistances, the

total or equivalent resistance of the circuit must be used.

You can use the formulas defined in these notes, but these are the most formal derivations of of

analysis of these circuits. I strongly recommend use of the rules we will cover in our examples in

class.

Series Circuit Rules1. In a series circuit the current has only one path to

follow. This means that the current is the same everywhere in a series circuit. This is an application of the law of conservation of charge and mass. We will verify this experimentally later.

2. For a series circuit with two resistors, RA and RB, according to Ohm’s Law the sum of the voltage drops across each resistor is equal to the total voltage in the circuit. This is an application of the law of conservation of energy.

3. Since there is only one pathway for the electrons to follow in a series circuit the equivalent or total resistance of the circuit is equal to the sum of the individual resistances.

Voltage Dividers

• A series circuit is called a voltage divider because the voltage from the source is split proportionately between the two (or more) resistors.

Series Circuit

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As the current goes through the circuit, the charges must USE ENERGY to get through the resistor. So each individual resistor will get its own individual potential voltage). We call this the VOLTAGE DROP.

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;Note: They may use the terms “effective” or “equivalent” to mean TOTAL!

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ExampleA series circuit is shown to the left. a) What is the total resistance?

b) What is the total current?

c) What is the current across EACH resistor?  

d) What is the voltage drop across each resistor?( Apply Ohm's law to each resistor separately)

R(series) = 1 + 2 + 3 = 6

V=IR 12=I(6) I = 2A

They EACH get 2 amps!

V12 V V3=(2)(3)= 6V V2=(2)(2)= 4V

Notice that the individual VOLTAGE DROPS add up to the TOTAL!!

Parallel Circuits

• A parallel circuit is called a current divider. Unlike a series circuit, current will divide when given multiple branches through which to propagate. The amount of current that passes through each branch is proportional to the resistance in each.

• Consider a parallel circuit with two resistors, RA and RB

If we consider wires to be perfect conductors (zero resistance) then this is like having both sides of each resistor touch opposite sides of the battery. This means there must be a voltage drop of V across both RA and RB.

Parallel Analysis Rules

1. Since each branch of the circuit is connected in parallel to the battery, each branch receives the same energy, thus has the same voltage.

Vbatt = V1 = V2 = V3 …

2. Current is split proportionately to the resistance of each branch, but the total is maintained in the circuit.

Itot = I1 + I2 + I3

3. Because current splits, equivalent resistance is less simple than series circuits

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Parallel Circuit

In a parallel circuit, we have multiple loops. So the current splits up among the loops with the individual loop currents adding to the total current

It is important to understand that parallel circuits will all have some position where the current splits and comes back together. We call these JUNCTIONS.

The current going IN to a junction will always equal the current going OUT of a junction.

Junctions OUTIN

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Electron flow notation

Parallel CircuitNotice that the JUNCTIONS both touch the POSTIVE and NEGATIVE terminals of the battery. That means you have the SAME potential difference down EACH individual branch of the parallel circuit. This means that the individual voltages drops are equal.

This junction touches the POSITIVE terminal

This junction touches the NEGATIVE terminal

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Example

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To the left is an example of a parallel circuit. a) What is the total resistance?  

b) What is the total current?  

c) What is the voltage across EACH resistor?   d) What is the current drop across each resistor? (Apply Ohm's law to each resistor separately)

2.20

3.64 A

8 V each!

9

8

7

8

5

8975 III

IRV

1.6 A 1.14 A 0.90 A

Notice that the individual currents ADD to the total.

Same

Compound (Complex) CircuitsMany times you will have series and parallel in the SAME circuit.

Solve this type of circuit from the inside out.

WHAT IS THE TOTAL RESISTANCE?

3.1133.3380

3.33;50

1

100

11

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RR

Compound (Complex) Circuits

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3.33;50

1

100

11

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PP

R

RR

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TTT

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I

RIV

)3.113(120

Suppose the potential difference (voltage) is equal to 120V. What is the total current?

1.06 A

What is the VOLTAGE DROP across the 80 resistor?

80

80

808080

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V

V

RIV

84.8 V

Compound (Complex) Circuits

AI

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What is the VOLTAGE DROP across the 100 and 50 resistor?

35.2 V Each!

50

2.35100

2.35

50

100

3&21)(

32)(

I

I

III

III

seriesT

parallelT

What is the current across the 100 and 50 resistor?

0.352 A

0.704 A

Add to 1.06A

Circuit Overload• A circuit becomes “overloaded” when extra

“load” or resistance is added. There are two general outcomes depending on the type of wiring present:– Series: Circuit shuts down/Current too low to

operate resistors– Parallel: Current becomes dangerously high,

wires melt, arc, things catch on fire.

Series Overload

Req = ?Req = ?

Generalize: As resistors are ADDED to a series circuit, the equivalent resistance of the circuit ________?________ .

Apply Ohm’s Law: For the same voltage source, as the equivalent resistance of a series circuit ________(same as above)________ , the current _____?_____.

Parallel OverloadReq = ?

Req = ?

Generalize: As resistive branches are ADDED to a parallel circuit, the equivalent resistance of the circuit ________?________ .

Apply Ohm’s Law: For the same voltage source, as the equivalent resistance of a parallel circuit ________(same as above)________ the current _____?_____.

What happens to the power dissipated by the circuit?How does this energy use manifest itself?

Why does it happen?• In household wiring, dangerous overload

normally occurs when too many appliances are plugged into the same outlet. – Since socket receptacles are wired in parallel,

imagine the possibilities when you plug in two 6 outlet power strips into the same outlet and fill up each power strip.

– Plug in appliances that draw high current (vacuum, blender, hair dryer) can sometimes be enough to overload that particular circuit.

Prevention/Safety

1) Don’t plug too many things into the same socket/electrical run.

2) Fuses

3) Circuit breakers

Fuses

• A fuse is a section of wire that is designed to melt with high current, breaking the circuit.– Ideally the fuse melts faster than the wires in

the circuit…ideally.– Usually the melting section of wire is

protected from the surroundings so it can ignite anything.

Fuses

Circuit Breakers• Circuit breakers are mechanical switches designed

to disconnect a circuit when current gets too large.– Household breakers usually use stored mechanical

energy (springs) that keep a swtch just barely shut, poised to pop the circuit open. Combined with a small electromagnet, the breaker triggers and pops the circuit to open (off) when current rises to large levels.

– Since the electromagnet is controlled by current, the higher the current, the more force.

– Generally failsafe unless a mechanical defect prevents the operation somehow.

Circuit Breakers

1) Actuator lever - used to manually trip and reset the circuit breaker. Also indicates the status of the circuit breaker (On or Off/tripped). Most breakers are designed so they can still trip even if the lever is held or locked in the "on" position. This is sometimes referred to as "free trip" or "positive trip" operation.

2) Actuator mechanism - forces the contacts together or apart.

3) Contacts - Allow current when touching and break the current when moved apart.

4) Terminals

5) Bimetallic strip.

6) Calibration screw - allows the manufacturer to precisely adjust the trip current of the device after assembly.

7) Solenoid

8) Arc divider/extinguisher

Household type breaker cross section