Electric Currents What is an electric current? What makes current flow?

Electric CurrentsWhat is an electric current?

What makes current flow?

An Electric Current is simply electrons traveling through a conductor

like currents in a river

Why does the water in a river flow?

PE

Gravity is pulling it down, but a general rule of thumb is that an object has a tendency to move towards positions of lower energy.

Water will stop flowing when there is no PE difference

This is also when the pressures are equal on both sides

Water will stop flowing when there is no PE difference

In order to keep water flowing we would need to maintain a difference in height

The water would have to be continuously pumped upward to keep it flowing

An electrical current is made up of little flowing charged particles.

What quantity tells you the Potential Energy certain of amount of charge (J/C).

Electric Potential (Volts)

In order to keep current flowing we need an electron pump.

1.5 V

A battery keeps current flowing by maintaininga voltage difference (until it “dies”)

e-

Zn(s) Zn2+(aq) + 2 e-

electrons are produced when the zinc “corrodes” at the anode

2MnO2(s) + 2 H+(aq) + 2 e- Mn2O3(s) + H2O(l)

electrons used up at the cathode

when all the zinc is used up, the battery is “dead”

The rate at which charge“flow” is measured in current

I =Qt

Electrical Current:amperes, amps, A

the amount of charge that flows through a wire (C)

in this amount of time (s)

1 amp is 1 coulomb per second

This equation is the “definition” of current

A dim (40 watt) light bulb draws about 1/3 of an amp. How many electrons pass through it in 1 sec.

How about if the current is 2/3 of an amp?

The greater the potential difference (pressure) the faster the flow of water.

The bigger the electric potential difference, the faster the flow of electrons.

As Voltage Current

Voltage is like electrical pressure

How does the size of the hole affect flow rate?

A small hole provides more RESISTANCE to water flow.

Electrical RESISTANCE of something (like a wire) is how much it resists electrons flowing through it.

It is measure in OHMS

The Electrical Resistance of an object depends on 4 things

1.) THE MATERIAL

Copper wire Glass rod

Which will have the higher resistance?

The Electrical Resistance of an object depends on 4 things

2.) The Length

Which will have the higher resistance?

Short Long

The Electrical Resistance of an object depends on 4 things

3.) The thickness

Which will have the higher resistance?

THICK

THIN

The Electrical Resistance of an object depends on 4 things

4.) The Temperature

The hotter an object the more it resists current.

When some materials are cooled WAY DOWN, they actually lose all resistance and become SUPERCONDUCTORS

How would the resistance be affected if the wire was stretched out.

100 x magnification of a light bulb filament,notice the “spiraled” spiral

Electrical Resistor are used to control the current in circuits

The resistance of a material (like a wire) depends on several things

R =L cross sectional area (m2)

length (m)resistivity of the material (m)

Temperat

coefficientper degree C

Silver 1.59 x10 -̂8 0.0061Copper 1.68 x10 -̂8 0.0068

Aluminum 2.65 x10 -̂8 0.00429Tungsten 5.6 x10 -̂8 0.0045Iron 9.71 x10 -̂8 0.00651Platinum 10.6 x10 -̂8 0.003927Manganin 48.2 x10 -̂8 0.000002Lead 22 x10 -̂8 ...Mercury 98 x10 -̂8 0.0009Carbon* 30(graphite)Silicon* 0.1-60 ... -0.07Glass 1-10000 x10 9̂ ...Quartz 7.5(fused)Hard rubber 1-100 x10 1̂3

Material

Resistivity

(m)

x10 1̂7 ...

x10 -̂5 -0.0005

Temperat

coefficientper degree C

Silver 1.59 x10 -̂8 0.0061Copper 1.68 x10 -̂8 0.0068

Aluminum 2.65 x10 -̂8 0.00429Tungsten 5.6 x10 -̂8 0.0045Iron 9.71 x10 -̂8 0.00651Platinum 10.6 x10 -̂8 0.003927Manganin 48.2 x10 -̂8 0.000002Lead 22 x10 -̂8 ...Mercury 98 x10 -̂8 0.0009Carbon* 30(graphite)Silicon* 0.1-60 ... -0.07Glass 1-10000 x10 9̂ ...Quartz 7.5(fused)Hard rubber 1-100 x10 1̂3

Material

Resistivity

(m)

x10 1̂7 ...

x10 -̂5 -0.0005

What is the electrical resistance of25 meters of 12 gauge copper wire.Which has a cross sectional area of 3.3 x 10-6 m2

at 20oC

How would the resistance be affected if the wire was stretched out.

R =L

In general as a material gets hotter, its resistance goes up.

T = o (1 + (T - To))

Temperat

coefficientper degree C

Silver 1.59 x10 -̂8 0.0061Copper 1.68 x10 -̂8 0.0068

Aluminum 2.65 x10 -̂8 0.00429Tungsten 5.6 x10 -̂8 0.0045Iron 9.71 x10 -̂8 0.00651Platinum 10.6 x10 -̂8 0.003927Manganin 48.2 x10 -̂8 0.000002Lead 22 x10 -̂8 ...Mercury 98 x10 -̂8 0.0009Carbon* 30(graphite)Silicon* 0.1-60 ... -0.07Glass 1-10000 x10 9̂ ...Quartz 7.5(fused)Hard rubber 1-100 x10 1̂3

Material

Resistivity

(m)

x10 1̂7 ...

x10 -̂5 -0.0005

What is the electrical resistance of25 meters of 12 gauge copper wire.Which has a cross sectional area of 3.3 x 10-6 m2 at 100 oC.

at 20oC

What causes resistance to electrons moving through a conductor?

What happens to their energy as they move through a wire or resistor?

applet

Are there any electrons in a copper wire which is not connected to a battery?

e-

In a neutral wire, an electron moves randomly but don’t really go anywhere

-+

Path of an electron in an electric field

drift speed distance

-+

Path of an electron in an electric field

drift speed

An electron has a total speed of about 1,500,000 m/sbut usually has a drift speed of about .0001 m/s

With a drift speed of about .0001 m/s

Why does it not take several minutes for the lights to turn on, when you hit the switch?

The wires are already full of electrons, when one enters one exits.

-+

The electron bumps into atoms in its path

This slows its drift speed, & is also why a wire gets hotwhen current passes through it.

The hotter the wire, the faster the random motion of the electron is.

The more frequently bumps into an atom, and loses drift speed.

(the greater the resistance)

Temp

Electron motion applet

-+

Path of an electron in an electric field

Which way would field lines point?

Resistor

Battery. The longer line is the higher potential side (+). You may not always be given the + and -.

+-

Ideal Wires, no resistance or voltage drop

Symbols you will see

switch

resistor

battery

+-

valve

Skinny tube

pump

switch

resistor

battery

+-

valve

Tube

pumpwater flow e- flow

Which way will electrons flow?

switch

resistor

battery

+-

+ flow

Important side note!

Even though it is really electrons that flow around the circuit,it was originally believed that + charges flowed instead.Which way would positive charges flow?

switch

resistor

battery

+-

e- flow

Important side note!

Conventional “current or I” flows from + to -.Or if electrons flow CW, then “current” is CCW.

I

switch

battery

+-

This way following the current flow, there is a voltage drop across the resistor.

Remember, positive charges flow naturally flow High(+) to low (-) potentials

IVoltage drop

switch

resistor

battery

+-

valve

Skinny tube

pumpwater flow “current”

Voltage lost through resistancePressure lost through resistance

Ohm’s Law

V= I R

Electric Potential (V)Current (A)

Resistance ()

Ohm’s Law (restated)

I= VR

As Resistance Current

As Voltage Current

VOLTAGE is like Electric Pressure

Voltage Drives Current!!

Your hair dryer is intended to run on 110 V.If you go to Europe an plug it into a 220 V outlet,what will happen.

A 10 resistor is connected to a 9 V battery,what will happen to the current if it is replaced with a 20 resistor?

A 9-volt battery is place on your wet tongue which has a resistance of about 3000 ohms. How many amps run through your tongue?

An air conditioner is rated for 15 Amps through on 120 V circuit, what is its resistance.

Why is the bird safely perched on a power line

Picture water flowing down a river with a little trench cut into the side. The flow rate of water through the little trench will be very little.unless….

If dam is placed here, there will be a pressure difference and current will flow through the trench. Now the least resistance is elsewhere.

A technician installs a bird diverter to keep condors away from points which may be grounded.

Amperage Chart

.001 A mild shock.005 A hurts

.015 A loss of muscle control

.100 A probable death

Dry skin has a resistance of about 500,000 WET skin has a resistance

of about 3,000

If you touch a 120 V circuit

low currenthigh current

In order for current to flow, a circuit must be made

Which circuits will have current?

Which light bulb(s) will light?

Which light bulb(s) will light?

Electric POWER

Power =Energytime

If you were looking for the power of a waterfall,

what 2 factors would determine it

the height of the falls,the change in PE of the water

the flowrate of the water

the change in PE of the electronthe flowrate of electrons

P =

For electric power, it is very similar

ICurrentAmp,C/s

VVoltage V, J/C

PowerJ/s(Watt, W)

P = I VWhat power is required to run an air conditioner which draws 15 ampson a 220 V circuit?

P = I V

V = I R&

P = I2R= V2

R

Since

P = I2R= V2

R

How much current is drawn from a 120 watt toaster with a resistance of 65 ohm?

What is the resistance of a 40 watt car headlight intended to run on 12V?

P = I2R

V2

RP =

P = IV A 40 watt bulb and a 100 watt bulb are each connected to a 120 V outlet.

Which draws the most current?

What has the greatest resistance?

Circuits Lab 1

Mental note next year, LIGHT BULBS CHANGE RESISTANCE when they are ON.

Electric Companies charge you per kW hr.

Power * time =

Energy * time =time

Energy

kW hrHow many Joules of energy is a:

AmerenUE charges .085$

kW hr

AmerenUE charges .085$

kW hr

How much does it cost you per day to run your home air conditioning,if it draws 30 amps from 120 V circuit and runs about 25% of the day?

Voltage from a 12 V battery (Direct Current or DC), until it dies or has too much draw from it at once.

Current

T

Current 0

Time

AC or alternating current

The US uses AC current at 60 Hz,what does that mean

Time

What happens to the current that flow through the wire?

At times the current is moving:left or right or not at all

Current 0

The electric company does not sell electrons

all they do is jiggle the electrons in your wires which requires ENERGY

When you get electric shock, its your own electrons that are shocking you!

If you were to connect 2 resistors together (or anything else) there are two ways to do it.

parallel

series

If batteries are connected together in series the voltage adds up

1.5 V

3.0 V

4.5 V

10 ft

10 ft

10 ftIf each pump could only produce enough pressure to lift water 10 feet.With 3 pumps connected in series….

If batteries are flipped they can cancel, which is why direction is important

0 V

1.5 V

If the 3 pumps were connected in parallel all on the ground

they could still only pump the water up 10 feet

1.5 V

1.5 V

1.5 V

If batteries are connected in parallel

Resistors in series and parallel

Which will be harder to push water through

Twice as hard

When resistor are positioned in series the total resistance just adds up

4 4

Equivalent resistance

8

4 8

4 8

12

12

1.5 V

What is the total current running through the circuit

4 8

.125 A

1.5 V

Because the current can only go in 1 path, the current through both resistors is the same

4 8

.125 A

.125 A

.125 A

.125 A

1.5 V

The total voltage drop across both resistors is

4 8

1.5 V

But OHM’s law can be used to find the voltage drop across EACH resistor (V=IR)

.5 V 1.0 V

.125 A

24 V

IN SERIES, the current is the same through both resistor. BUT the bigger resistor has a greater voltage drop and consumes more power

4 8

EnergyEnergy

EnergyEnergy

A lamp with a resistance of 360 and another that is 144 are connected in series to a 120 V circuit. Which burns brighter?

9 V

3 light bulbs each with a resistance of 2 , are connected to a 9V battery. What is the current and voltage at each point along the circuit

Which bulb is the brightest?

9 V

What happens if one bulb burns out?

9 V

If a bulb burns out when connected in series, it is an open circuit (no flow).

9 V

What happens to the brightness of a bulb, if another is connected in series.

9 V

?

9 V

The bulbs are dimmer, the same voltage with more resistance means…

9 V

less current

Resistors are different from batteries when connected in parallel

Which “circuit” will be harder to flow through?

There are Twice the paths open to the water

The resistance is only 1/2 , so twice as much water will flow

4 4

4

Resistors can also be added in Parallel

Which circuit has the higher Resistance to current flow?

4

4

4

Equivalent Resistance

4

4

4

4

2

4/3

R1

R2

R3=

REQ

REQ

1= R1

1+ R2

1+ R3

1+ etc…

4

4

4

Equivalent Resistance

4

4

4

4

2

4/3

1= 4

1+4

1

1= 4

1+4

1+4

1

4

8

12

What is the equivalent resistance

9 V

What is the total current?

REQ=2.2

Is the current the same through each resistor?

Will the flow rate be the same through both tubes?

Both tubes are fed the same pressure

4

8

12

9 V

I1 = 4.09 A

REQ=2.2

What is the current through each resistorOHMS law can be used here as well!!

4

8

12

9 V

What would happen the the Voltage, Current, and Resistance if another resistor was added in parallel?

9 V9 V

How does the brightness change if another bulb is added in parallel?

What changed?

½ Resistance

Twice current

battery drains twice as fast

9 V

What if one burns out?

9 V

What if one burns out?

Are the headlights of a car wired in series or parallel?

A lamp with a resistance of 360 and one that is 144 are connected in parallel to a 120 V circuit. Which burns brighter?

Hot From Power company

Circuit Breakeror fuse (15 A)

to other circuit breakers

7 AFridge unused outlet

8 AmpMicrowave

Hot From Power company

Circuit Breakeror fuse (15 A)

to other circuit breakers

7 AmpFridge

8 AmpMicrowave

1 Amplight

Circuit Breakeror fuse (15 A)

to other circuit breakers

7 AmpFridge

8 AmpMicrowave

1 Amplight

Hot From Power company

9 V

Have you ever noticed when an additional light is turned on sometimes the lights dim?

When batteries are involved, this is because a battery has an internal resistance. “Ideal batteries” have none and maintain a constant voltage.

But in real batteries, the reactants have to diffuse through all the muck to reach an electrode and keep voltage up.

6 V

10

2

Usually internal resistance of a battery will be shown as a dashed box around it. It is NO DIFFERENT from any other resistor. How much current will flow through the circuit?

In most problems it will be ignored as they will be ideal batteries

6 V

10

2

EMF (electromotive force) is a relic term. It is Voltage you would measure across a battery under NO load.

It is usually abbreviated as E.M.F or emf or

6 V = EMF

10

2

The EMF in a case like this will be the voltage indicated.

Internal resistance

12 V

Under no load the voltage across the terminals of the battery will be 12 V (the EMF)

12 V

10

2

Terminal Voltage is what is left over for the rest of the circuit under the load as measured across the terminals of the battery

12 V

10

2

What is the terminal voltage here?

The terminals on a battery. Which way does current flow?Which way do current electrons flow?

6 V

10

2

What happens to the terminal voltage, if the 10 resistor is replaced by a 5 resistor?

What happens to the current flow?

What happens to the power dissipated by internal resistance?

MIXED Series / Parallel circuits

What is the equivalent resistance of the circuit below

4 2

6

4

4 4

4

4 4

What is the equivalent resistance of the circuit below

Kirchoff’s Rules

#1 Junction RuleCurrent In = Current Out

#2 Loop RuleThe sum of voltage (changes) around a closed loop must add to zero

#1 At ANY junction Current In = Current Out

I1 I2

I3

(I1 + I2 = I3 )

I1

I2

I3

If you guess the wrong direction, no big deal your answer will be negative. Just realize the current if flowing the opposite way. OK

+ -

#2 The sum of voltage changes around a loop must add to zero

On a roller coaster, you go up and down BUT end up back at the same height!!

StartFinish

4

-.5 V - 1.0 V

8

+ 1.5 V

Go for a walk around a track and end up at the same place

-.5 V + -1.0 V + 1.5 V = 0

4

-.5 V - 1.0 V

8

+1.5 Va

cdV

olta

ge (

V)

a b c d

1.5 V

0.5 V

e

b

e a

With the current, voltage drops by IR

I= 2 A

R= 3 -6 V

Some things to watch for when using the 2nd Rule,If you are moving around the loop across a resistor …

Some things to watch for when using the 2nd Rule,If you are moving around the loop across a resistor …

With the current, voltage drops by IR

I= 2 A

R= 3 -6 V

Against current, voltage increases by IR

I= 2 A

R= 3 +6 V

Uphill on the battery (- to +) +9V

Some things to watch for when using the 2nd Rule,If you are moving around the loop across a battery…

9 V

Uphill on the battery (- to +) +9V

Some things to watch for when using the 2nd Rule,If you are moving around the loop across a battery…

9 V

Down hill, ( - to +) -9V

9 V

200 V

20 V

60 V80 V

20 V

60 V

20 V

The sum of the changes around ANY loop adds up to ZEROLets which are positive and which are negative as we follow a loop(there are 3 paths to follow and their reverses)The drops are indicated, find the voltages at each node

I

I

I

II

I

Two basic approaches to solving circuit problems

A single battery- break it down into simpler and simpler picturesUse the “right” picture to find each answerjust use V=IR to find what you need

Multiple battery (complex circuit)-Label +/- on batteryAssign a direction to current in each branchPick a junction and apply Junction RuleApply Loop RuleKill the Algebra

120 V

10 80

40

I1

I2

I3

V=_____

= 3.3 Amp

87 V= 1.1 Amp

= 2.2 Amp

REQ =_____36.7

4

6

10

2

Find REQ, and I’s

20

40

I3

I2

12 VI1

REQ = 9

=1.33 A

9.3 V

=0.93 A

=0.40 A

4

6

10

2

Find Potentials

20

40

I3

I2

12 VI1=1.33 A

9.3 V

=0.93 A

=0.40 A

___

___

3.7 V

5.3 V

More examples at end of show if needed

30

40

Find the currents and the voltages at the given positions. Note if you guess a current direction the wrong way, no sweat it will just be negative so it is opposite your guess.

(note to bernabo see page 566 of giancoli to check)

1

I1

I2 80 V

45 V

20

I3

a b c d

efg

h

1

40

20

5

15

10

12 V

Which method would I use here to find current through each resistor?

40

20

5

15

10

12 V

What can I break down here?

NOTHING.that pesky 5 resistor!!!

40

20

5

15

10

12 V

Use method #2, UGHHH

I1+ -

I2

I3 I4

I5

I6

A minor side note.

Meters are used to measure current and voltage difference.

A voltmeter measures voltage

An ammeter measures current.

This is a modern multimeter, which can measure current, voltage, resistance, capacitance, frequency…..

4 8

+ 1.5 V

-1.0 VWhen measuring VOLTAGE

The ends just act like probes and don’t affect the circuit.

They measure the voltage difference.

The meter is not part of the circuit.

Safe, I can stick the ends in an outlet!

4 8

+ 1.5 V

.125 AWhen measuring Current

The meter acts like a wire in the circuit.

All the current flows through the meter.

DO NOT stick in outlet!!!

A standard current single instruments can measure most anything..But based on convention something that measures…

Amperage is a AmmeterIt must be in thepath it measures

Voltage is a voltmeter.It measures from the sidelines

A

V

120 V

10 80

40

A

V

If you see these in a circuit they don’t affect the circuit, they are just asking you to “measure” the voltage difference or current

The symbol below shows a ground wire

It tells you that the voltage at that location is 0

12 V

15 80

40

And another “trick” you might see,What is the current flowing through the 10 resistor?

12

10

Back to capacitors, why are capacitors useful?

They store electric energy

Flux capacitor capable of discharging 2.21 jiggawatts

Initially the metal pieces are neutral but when connected to a battery (or other voltage source)

+- +

-+- +

-

1.5 V

1.5 V

Whatever idiot made this thinks the electrons move

The electrons will stay put when the battery is removed. But now there is an electric field and energy is stored in the electric field

+-

+-

+- +

-

1.5 V

When connected again the electrons flow (& do work)

+-

+-

+- +

-

1.5 V

C =K0A

dRemember the capacitance increases with the area of the plates

UE = 2CV2 Capacitance is important, because it

increases the amount of energy that can be stored for a given battery connected to it (voltage source)

Q = CV However, Q= CV is the primary equation we will use here!

--

+-+

-

1.5 V

++

--

+-+

-++

How are these capacitors connected?Series or Parallel

--

+-+

-

1.5 V

++

--

+-+

-++

Connecting them in parallel, is just like doubling the area.

What is the voltage difference across each plate?

--

+-+

-

+

++

+

--

+-+

-

1.5 V

V

C1

C2

C3

Ceq = C1 + C2 + C3 etc…

Each capacitor reaches battery voltage difference

V

C1C2 C3

Ceq

+ -

+ -

+ -

+ -

+ -

+ -+ -+ -

C1C2 C3

=1

+1

+1 1

Voltage difference is shared between capacitors

SeriesParallel

-

+-+

1.5 V

++

-

+-+ ++

---

-

-

Before the battery is connected, the plates are all neutral

-1 +1 -1 +1

-

+-+

1.5 V

++

-

+-+ ++

- - --

When connected in series because the current must be the same,All the capacitors must end up with the same charge!!!

-1 +1 -1 +1

V

C1

C2

C3

V

C1C2 C3

Parallel capacitors must have equal voltages Series capacitors

must have equal charge stored

10 V

20 F

50 F

10 F

What is the equivalent capacitance of the 50 & 10 F capacitors?

Some resources want you to find the charge on each capacitor. I can’t find any decent worked examples though. And there are a LOT of conceptual pitfalls here. Not worth going here. (note to mr. b)

RC Circuits

Capacitors and resistors are often used together.

VS

R C

When the switch is closed, current begins to flow charging the capacitor.

When the capacitor reaches 12 V, the current flow stops.

V = 12 VS

R C

Animation of capacitor charging and discharging.

Graph of current running through an RC circuit when switch is closed

At first, the capacitor acts like a wire with no resistance.

After “a long time”, a capacitor acts like an infinite resistor

100 VC

20 15

10 5

What is the current and power delivered by the batteryWhen the switch is first closed?After the switch has been closed for “a long time”.

S

R C

What would a graph of current vs. time look like if a charged capacitor were connected to a resistor?

4

6

10

2

What are the voltage drops across each resistor and voltages at each point?

20

40

I3

I2

9 VI1

Another exampleIf needed

4

15

10

4

20

40

I3

I2

24 VI1

V= V=

V= V=

Another exampleIf needed