the flow ofthe flow of charged particlescharged particles;

can be positive or negative,but usually negative (electrons)

through a conducting metal

electric cell - a device thatconverts one form of energy

to electrical energy

Chemical cells convert chemicalenergy into electrical energy.

Chemical cells can be“wet” or “dry”.

SolarSolar cellscells convert light energyinto electrical energy.

A generatorgenerator converts mechanicalenergy into electrical energy.

batterybattery - two or more cellsconnected in series or in parallel

Electric current is measuredin Amperes, in honor ofAndre Marie Ampere.

One Ampere is the flow ofOne Ampere is the flow ofone Coulomb of charge per second.one Coulomb of charge per second.

1 Amp = 1 Coulomb per second = 1 C/s1 Amp = 1 Coulomb per second = 1 C/s

II = QQ/tt

AmmeterAmmetera device that measures current

VoltmeterVoltmetera device that measures

electric potential difference

powerpower = = workwork//timetime

= (= (workwork//chargecharge))..((chargecharge//timetime))

== electric potential differenceelectric potential difference ..

currentcurrent

PP ( (WattsWatts) = ) = VV ( (VoltsVolts))..II ( (AmpsAmps))

Analogies of simple circuits are these links:Analogies of simple circuits are these links:

Water circuit analogy Water circuit analogy linkAir flow Air flow link

ResistanceResistance

determines the amount of current flowdetermines the amount of current flow

= the ratio of potential difference to current= the ratio of potential difference to current

RR =VVII

The SI unit of resistance is the OhmOhm, , namedin honor of Georg Simon Ohm.

One OhmOne Ohm of resistance is the resistancesuch that one Voltone Volt of potential differenceis needed to obtain a current of one Ampone Amp.

The resistance of a circuit element depends on:

1. the length of the conductorthe length of the conductoras length increases, resistance increases proportionally

2. the cross-sectional area of the conductorthe cross-sectional area of the conductoras area increases, resistance decreases proportionally

3. the resistivity of the conductorthe resistivity of the conductoras resistivity increases, resistance increases proportionally

Ohm’s LawOhm’s LawThe ratio of potential difference to currentThe ratio of potential difference to current

is constant.is constant.

If R = V/I is a constant valueIf R = V/I is a constant valuefor a given resistor, then thatfor a given resistor, then that

resistor is said to obey Ohm’s Law.resistor is said to obey Ohm’s Law.

Click Click here and and here to link to pages describing resistor to link to pages describing resistorcolor codes.color codes.

ResistivityResistivityThe resistivity, , of a conductor is equal to the

resistance of a wire 1 cm long and having a cross-sectional area of 1 cm2.

RR

RR = resistance, measured in Ohms = resistance, measured in Ohms

=

= resistivity, usually in units of = resistivity, usually in units of cmcm

ll

l = length, measured in cml = length, measured in cm

AA

AA = cross-sectional area, measured in cm = cross-sectional area, measured in cm22

Click Click here and and here to run to runsimulations of Ohm’s Law.simulations of Ohm’s Law.

Many circuit elements do notMany circuit elements do notobey Ohm’s Law. Resistorsobey Ohm’s Law. Resistorsthat get hot, like light bulbsthat get hot, like light bulbsand heating elements, do notand heating elements, do notkeep a constant resistance. keep a constant resistance. Resistance generally Resistance generally increases as increases as objects become hotter.objects become hotter.

Resistor CircuitsResistor CircuitsSeries

1. 1. total resistancetotal resistance is the sum of the is the sum of the separate resistorsseparate resistors

RRTT = R = R11 + R + R22 + R + R33 + ... + ...

2. 2. currentcurrent is the same through each resistor is the same through each resistor

IITT = I = I11 = I = I22 = I = I33 = ... = ...

3. 3. total potential differencetotal potential difference is the sum of each is the sum of each

VVTT = V = V11 + V + V22 + V + V33 + ... + ...

In other words, in a series circuit,In other words, in a series circuit,resistance and voltage add,resistance and voltage add,but current stays the same.but current stays the same.

RR11

RR22

RR33

EE = 12 V = 12 V

RRTT = =

VVTT = =

IITT = =

RR11

RR22

RR33

V,V,VV

PPTT = =

R,R,

I,I,AA

P,P,WW

8.0

5.0

2.0

RR11

RR22

RR33

EE = 12 V = 12 V

RRTT = 15 = 15 ΩΩ

VVTT = 12 V = 12 V

IITT = 0.80 A = 0.80 A

RR11

RR22

RR33

V,V,VV

PPTT = 9.6 W = 9.6 W

R,R,

I,I,AA

P,P,WW

8.0

5.0

2.0

0.80

0.80

0.80

6.4

1.6

4.0

5.1

1.3

3.2

Parallel 1.1. reciprocal of the total resistance reciprocal of the total resistance is is

the the sum of the reciprocals of the sum of the reciprocals of the

separate separate resistorsresistors

1/R1/RTT = 1/R = 1/R11 + 1/R + 1/R22 +1/R +1/R33 + ...+ ...2. 2. total currenttotal current is the sum of the current is the sum of the current

through each resistorthrough each resistorIITT = I = I11 + I + I22 + I + I33 + ... + ...

3. 3. potential differencepotential difference is the same is the same across across each resistoreach resistorVVTT = V = V11 = V = V22 = V = V33 = ... = ...

In other words, in a parallel circuit, resistance adds as reciprocals,

voltage stays the same, and current splits.

In other words, in a parallel circuit, resistance adds as reciprocals,

voltage stays the same, and current splits.

EE = 12 V = 12 V

RRTT = =

VVTT = =

IITT = =

RR11

RR22

RR33

R,R,

V,V,VV

I,I,

PPTT = =

RR33

RR11

RR22

P,P,WW

12

8.0

12

EE = 12 V = 12 V

RRTT = 3.42 = 3.42 ΩΩ

VVTT = 12 V = 12 V

IITT = 3.50 A = 3.50 A

RR11

RR22

RR33

R,R,

V,V,VV

I,I,

PPTT = 42 W = 42 W

RR33

RR11

RR22

P,P,WW

12

8.0

12

12

12

12

1.0

1.5

1.0

12

12

18

Go to Go to link1, , link2, , link3, , link4, link5, and link6 to view, link5, and link6 to viewpages and simulations examining pages and simulations examining

Kirchhoff’s Loop and Junction Rules.Kirchhoff’s Loop and Junction Rules.

Kirchhoff’s RulesKirchhoff’s Rules

Loop Rule: Loop Rule: The sum of the potential differencesThe sum of the potential differencesaround any closed circuit loop is zero.around any closed circuit loop is zero.

Junction Rule: Junction Rule: The sum of the currentsThe sum of the currentsinto any circuit junction is zero.into any circuit junction is zero.

The site linkedThe site linkedhere allows youhere allows youto build and test to build and test your own series,your own series,parallel, and/orparallel, and/orcombination circuits.combination circuits.

For a complete interactive tutorial onFor a complete interactive tutorial onelectricity and magnetism, go here.electricity and magnetism, go here.