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# Electrical circuits

## 1.

Electrical CircuitsALESSANDRO VOLTA

(1745-1827)

ANDRE MARIE AMPERE

(1775-1836)

GEORG SIMON OHM

(1789-1854)

## 2.

Sources of Voltage (Energy)Voltage, also

known as

“electromotive

force” can be

create by

many sources

of energy

solar

geothermal

wind

biomass

nuclear

hydroelectric

chemical

piezoelectric

ALLESANDRO VOLTA AND THE ELECTRIC BATTERY

A VOLTAGE SOURCE IS LIKE A WATER PUMP

## 3.

Electrical CurrentCurrent is the rate of flow of charge through a conductor.

charge

current

time

I

q

t

Current flow is defined in the

direction of positive charge;

since electrons flow in wires,

current is opposite the flow of

electrons.

SI

units

1coulomb

1 amp

1 second

C

A

s

Small microamp ( A) currents

flow through your body, but

larger amounts of current are

dangerous, even deadly.

CURRENT

EFFECT

0.0001 A

threshold of feeling

0.001 A

mild shock felt

0.005 A

shock is painful

0.015 A

muscle control is lost

0.100 A

death can occur

## 4.

Electrical CurrentPotential difference creates an

electric field in a circuit. The

electric field induce charge to flow.

Moving electrons collide with

vibrating atoms, so they zigzag in

a random path, with a slow

click for

forward drift velocity.

animation

Although the electric field travels at near the speed of light, the

drift velocity of electrons is less than a millimeter per second.

Electrons do not race around a circuit!

## 5.

Electrical ResistanceResistance is a measurement of a material’s ability to resist

the flow of electrical charge.

voltage

resistance

current

V

R

I

SI 1 ohm 1 volt

units

1 amp

Resistivity depends on the nature of a material. Conductors

have low resistivity and insulators have high resistivity.

Resistance depends on

the material’s type,

length, cross- section,

and temperature.

click for

resistance

codes

resistance

applet

V

A

## 6.

Alternating versus Direct CurrentThomas Edison brought direct current

to the masses. Nikola Tesla proved

alternating current to be more efficient.

Alternating current (ac) switches the

direction of the current back and forth

at 60 times per second (60 Hertz).

DIRECT CURRENT

North America uses ac for its power

grid because it was safer and more

reliable when infrastructure began.

Batteries provide direct current (to

increase battery life).

Most devices use direct current so a

transformer converts ac to dc often at

lower voltage.

Direct energy conversion devices like

light bulbs, heaters, can run off ac or dc

ALTERNATING CURRENT

click for animation

## 7.

Ohm’s LawElectrical circuit versus a water circuit

click for

animation

click for

animation

slope = 1/R

voltage

OHMIC

cu

rr

en

t

cu

rr

en

t

cu

rr

en

t

When a device shows a linear relationship between

voltage and current, it is said to be “ohmic”

slope = 1/R

voltage

NONOHMIC

slope = 1/R

voltage

ONE-WAY (DIODE)

## 8.

Energy, Power, and Cost in CircuitsPOWER LAW

power

energy charge voltage

current voltage

time

time

P I V

Combine Power Law with Resistance equation

P I V I(IR)

P I R

2

V

P I V

V

R

( V )2

P

R

Cost of Electrical Power

energy power time

Example - Find the cost of a 1500 watt hair dryer run for

12 minutes, using the rate of $0.10 per kilowatt hour.

cost rate energy

energy in kilowatt hours (kW h)

cost in dollars ($)

time in hours (h)

$

rate in dollars per kilowatt hours

kW h

1 kW

1.5 kW

10 3 W

1h

time 12 min

0.2 h

60 min

power 1500 W

cost 0.10

$

kW h

(1.5 kW) (0.2 h)

cost $0.03 or 3 cents!

## 9.

Kirchoff’s RulesRule #1 - The Loop Rule

A statement of

conservation of energy

-4 v

The sum of the potential

differences (voltages) around

any closed loop in a circuit

must be zero

-2 v

example

+12 v

Rule #2 - The Junction Rule

A statement of

conservation of charge

The current entering a

junction in a circuit equals the

current leaving the junction

2A

10 A

3A

5A

example

-6 v

## 10.

Series CircuitsA series circuit has only one pathway around the circuit

Rule # 1 means that the voltage

across all resistors in series must

add up to the source voltage

V

V11

V22

V33

Rule # 2 means that the current

through all resistors in series

must equal the source current

I I1 I2 I3

Combine the two equations:

V V1 V2 V3

I

I1

I2

I3

Req R1 R2 R3

click for

animation

## 11.

Series Christmas Tree LightsSeries wiring was often used for Christmas tree lights

One bulb burns out, they all go out!

Who’s to say which one burned out!

Modern bulbs use a “jumper” wire.

This wire has insulation around it.

When the bulb burns out, the

jumper now has 120 volts across it.

The voltage produces a spark, and

the insulation burns off. The circuit

is now complete, with the one bulb

not lit but easily replaced.

## 12.

Parallel CircuitsA parallel circuit has multiple pathways around the circuit

Rule # 1 means that the voltage

across all resistors in parallel

must equal the source voltage

V V1 V2 V3

Rule # 2 means that the current

through all resistors in parallel

must add up to the source current

I I1 I2 I3

Combine the two equations:

I

I1

I2

I3

V V1 V2 V3

1

1

1

1

Req R1 R2 R3

click for

animation

click for

animation

## 13.

click foranimation

Combination Circuits

click for

animation

A combination circuit must be simplified into groups of series and

parallel resistors, and then the equivalent for each group is then found.

Req 10 2 12

1

1 1

= +

Req = 3

Req 12 4

Req =1+2 +3 + 4 =10

## 14.

Combination CircuitsThe total current in the combination circuit is determined and used to

work “backwards” to find other branch currents and resistor voltages.

V

120 v

I

12 A

Req 10

Find current through circuit

I V / R 36 /12 3 A

Find current through 12 equivalent

V IR 12 3 36 v

Find voltage across 3 equivalent

V IR 3 2 6 v

Find voltage across 2 resistor