Ch 18: Electric currents

Charges in motion

How is this different from

static?

• Recall that a buildup of charges on an object is called Static electricity. This buildup will continue until an opportunity for discharge arrives. THEN we SEE the discharge as a spark (light lightning)

• In 1752 Benjamin Franklin’s famous “kite experiment” showed that lightning is an electric discharge- a giant spark.

Steady now…

• The transition from static electricity to flow of electric charge was sparked by the invention of the electric battery by Alessandro Volta (1745-1827) in 1800.

• The steady electric current flowing from this source transformed our civilization.

Electric Battery• The discovery of the battery came about as a

result of an argument between Luigi Galvani and Volta. In the 1780s Galvani connected 2 different metals to a frog’s leg muscle and a static electricity machine.

• Volta proved that the electricity was not due to the animal cells, but rather due to two different metals using the frog’s leg as an electrolyte. The source of the electricity was in the different metals.

Alessandro Volta’s Pile (Battery)

• Volta found certain combinations of metals produced greater effects than others. He listed an “electrochemical series” and found carbon could be used in place of one metal.

• He put a piece of cloth soaked in a salt solution between 2 metals and piled a “battery “ of such couplings on top of each other. This “pile” or “battery” produced much more potential difference.

Volta leads the

way

• Scientists eventually realized the battery produces electricity by transforming chemical energy into electrical energy.

• Simplest batteries contain 2 plates (different metals) called electrodes, immersed in a solution called the electrolyte. This is called an electric cell.

• Several cells connected together is called a battery.

How does the battery cell work?

• The electrodes “dissolve” in the acidic electrolyte. Zn leaves behind 2 electrons and enters the solution as “positive”. The zinc electrode then acquires a “negative charge”.

• As the solution becomes more positive, it pulls electrons off the carbon electrode, making it acquire a “positive charge”.

• Opposite charges develop a potential difference between the terminals and this is maintained until a conductor is connected between them. (See pg 529)

How long will charge flow?

• After some time, one of the electrodes is used up and the cell becomes “dead”.

• The voltage between the battery terminals depends on what materials are used and their ability to be dissolved or give up electrons.

• Connecting batteries so the positive terminal of one touches the negative terminal of the other is in “series” and their voltages add up.

Electric Current

• An electric circuit is a continuous conducting path between the terminals of a battery.

• A battery symbol is represented by

• Longer line = positive terminal, shorter = negative terminal.

• A flow of charge through the battery and wires of a complete path is called electric current.

Charge it up

• Electric Current in a wire is the net amount of charge that passes through a wire per unit of time at any point.

• Average current, I is defined as where Q is the charge passing through the conductor in any time interval t.

• Electric current is measured in coulombs/second or amperes (abbrev amps or A).

IQ

t

Conservation of Charge

• Charge doesn’t disappear when it flows through a circuit.

• For any single circuit, the current at any instant is the same at one point as it is at any other point. This is the Conservation of Electric charge.

• Current is the flow of charge through a circuit.

Example 18-1

• A steady current of 2.5A flows in a wire for 4.0 min. (a) How much charge passed through any point in the circuit? (b) How many electrons would this be?

18-1 Solution

• (a) Since the current was 2.5A or 2.5 C/s, then in 4.0 mins (=240 seconds) the total charge that flowed was

• ΔQ = (2.5 C/s) (240s) = 600 C

• (b) The charge on one electron is 1.60x10-19 C so 600 C would consist of

tIQ

electronsxelectronCx

C 21

19108.3

/106.1

600

See Conceptual Ex 18-2

• What’s wrong with each scheme in trying to light a light bulb with a flashlight battery and a single wire? You try it…

• How many ways can this be done? Choose a partner and figure it out.

Conduction, duction what’s

your function?• Conductors contain many free electrons.

• When a potential difference (voltage) is established across a circuit (complete closed conducting path), it is electrons that actually flow in the wire.

• Conventions of electric current many years ago decided conventional current is the direction positive charge will move. (From + to -) but is equal to the negative charge flowing from – to +.

Ohm’s Law: Resistance and Resistors

• Georg Simon Ohm (1787-1854) was the first to establish experimentally that current, I, is directly proportional to the potential difference, V, applied to the ends of a wire.

• One source of potential difference is a battery.

Current flowin’

• Compare current in a wire to the flow of water in a river or pipe. In order to get current to “flow” a difference in potential between the ends must exist. (ie tip the pipe, gravity pulls water downhill.)

• How much current flows in a wire depends on the voltage, but also on the resistance. More resistance, like junk in a river, means less current.

Ohm’s Law: IV

ROhm’s Law establishes a

relationship between

current, voltage, and

resistance in a circuit.

Current, I, is equal to

Voltage / Resistance.

Resistance is measured in

ohms.

Current is measured in

amps.

Potential difference is

measured in volts.

Example 18-3 Bulb Resistance

• A small flashlight bulb draws 300mA from its 1.5 V battery. (a) What is the resistance of the bulb? (b) If the voltage dropped to 1.2 V, how would the current change?

18-3 Solution

• (a) We use Ohm’s law and find R=V / I

• R = 1.5 V / 0.30 A = 5.0 Ω

• (b) If the resistance stayed constant, the current would be approximately I = V / R

• I = 1.2 V / 5.0 Ω = 0.24 A

More on Resistance

• All electronic devices from wires to heaters to stereo amplifiers to lights offer resistance to the flow of current.

• In many circuits, resistors are used to control the amount of current.

• Two main types of resistors are wire wound resistors and composition resistors (which have color codes marking levels of resistance.)

Your turn to Practice

• Please do ch. 18 Review pg 551 #s 1-10

Resistivity

• Resistance of a wire is directly proportional to its length, L and inversely proportional to its cross-sectional area, A. (A thicker wire has less resistance because there is more room for electrons to pass and a longer wire has greater resistance because there are more obstacles to electron flow.

• The third factor is a proportionality constant, ρ, called resistivity, and depends on material type.

• Low R = good conductor. RL

A

Ex 18-4 Speaker Wires

• Suppose you want to connect your stereo to remote speakers. (a) If each wire must be 20m long, what diameter of copper wire should you use to keep the resistance less than 0.10Ω per wire? (b) If the current to each speaker is 4.0A, what is the voltage drop across each wire?

18-4 Solution

• (a) We solve for the area A and use table 18-1

• The cross-sectional area of a wire is related to its diameter by A=πd2/4. The diameter must then be at least

• (b) From Ohm’s Law, V=IR = (4.0A)(0.10Ω)= 0.40 V

AL

R

(1.68x10 8 *m)(20m)

(0.10 )3.4x10 6m2

d4A

2.1x10 3m 2.1mm

Resistivity

• The resistivity of a material depends on temperature in that resistance of metals increases with temperature. At higher speeds, atoms are moving faster and interfere with each other more with the flow of electrons.

• There is a temperature coefficient of resistivity, α, that is given in Table 18-1 for various materials.

Electric Power

• Electric energy can be transformed into other forms of energy such as thermal energy or light because the current is large and many collisions occur in tiny wire filaments or heating elements. (Low resistances of up to a few hundred ohms)

• During collisions KE of atoms increases and thus temperature increases.

Electric Power

• Power is the rate at which energy is transformed. P = (QV)/t.

• Recall charge flowing per second is current I=Q/t so it follows that Power = I * V

• SI unit of Power is the same for any kind, watt. (1W=1J/s)

• P=IV = I(IR) = I2R = (V/R)*V = V2/R

• Remember “PIVVIR” : P=I*V, V=I*R

Ex 18-7 Headlights

• Calculate the resistance of a 40 W automobile headlight designed for 12 V.

• SOLN: R = V2/P

• R = (12V)2 / (40W) = 3.6Ω

• This is the resistance when the bulb is burning brightly at 40 W. When the bulb is cold, the resistance is lower and since the current is high, most bulbs burn out when first turned on.

Electric Energy

• Our electric bill costs us money based on the electric energy we use, not just power.

• Since Power is the rate energy is transformed, electric energy is just Power * time the power is used.

• E=P*t (kilowatt*hours) 1kWh=1000W*3600s =3.6x106 J.

Ex 18-8 Electric Heater

• An electric heater draws 15.0A on a 120 V line. How much power does it use and how much does it cost per month (30days) if it operates 3.0 h per day and the electric company charges 10.5 cents per kWh?

• Solution: P=IV = (15.0A)(120V)= 1800 W

• To operate per month (3h/d)(30d)=90hrs so it would cost (1.80kWh)(90h)($0.105)=$17.

Ex 18-9 Lightning Bolt

• A typical lightning bolt can transfer 109 J of energy across a potential difference of perhaps 5 x 107 V during a time interval of 0.2s. Use this information to estimate the total amount of charge transferred, the current, and the average power over the 0.2s.

18-9 Soln

• Energy =QV so

• The current over the 0.2s is about

• The average power delivered is Pavg = energy/time

• Which can also be found by P=IV=100A(5x107 V)=5GW

CVx

JQ 20

105

107

9

As

C

t

QI 100

2.0

20

GWWxs

JP 5105

2.0

10 99

Power in Household Circuits

• If current in wires gets too large, the wires get hot (produce thermal energy at a rate of I2 R). Wires in walls of a building can get so hot & start a fire.

• Buildings should be designed to handle any expected load & prevent “overloading”. (Carrying more current than is safe)

• Fuses and circuit breakers are devices used to help prevent overloading. This occurs when too many devices draw current in that area OR when wires are faulty.

Household Power

• Household circuits are designed so every device connected receives the standard voltage (120V in the US).

• These circuits are typically arranged “parallel” (more later).

• Total current in a circuit that “blows” should be checked!

• Never replace a properly rated fuse with a higher one!

Open circuits

• A blown fuse or breaker will “open” a circuit so there is no longer a complete conducting path and current will not flow.

Alternating Current

• When a battery is connected to a circuit, current flows steadily in one direction. This is called direct current, DC.

• Electric generators (power plants) produce alternating current, AC.

• AC reverses directions many times each second and is sinusoidal (creates sine wave) Current supplied to homes and businesses around the world is ac.

AC

• AC voltage oscillates between –V0 and +V0 where V0

is referred to as peak voltage.

• As a function of time, the voltage can be found by V=V0 sin2πft.

• The frequency, f, is the number of complete cycles per second and in the US and Canada is 60 Hz. Some countries use 50Hz.

Your turn to Practice

• Complete the wksh for series circuits given in class.

• Please do Ch 18 Review pg 551 #s 11, 12, & 13

• Please do Ch 18 Review pg 552 #s 23, 24, & 27