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Electric Current and Circuits
Moving Charges
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Static charges will move if potential
difference and conducting path exists
between two points
Electric field due to potential difference
creates force on charges
Charged capacitor can discharge and
move charges but only until potential
on plates is equal
Moving Charges
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In solids, moving charges are electrons
In liquids and gases, both positive and
negative ions can move
Electrolyte: substance whose aqueous
solution conducts electric current
Positive charge moving one direction is
equivalent to negative charge moving in
opposite direction
Electric Current
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Rate of flow of electric charge through a
cross section of a conductor
Unit is ampere (A or amp); 1A = 1C/s
Ampere is a fundamental unit of SI system
Electrons flow from negative to positive
Conventional current is flow of positive
charges from positive to negative (thank you
Ben Franklin)
Electron Drift Speed
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Electrons are pushed by electric field
established in conductor
Electrons possess thermal velocity ~ 106
m/s, causes random collisions with atoms
Speed due to electric field much less ~
10-4 m/s, called drift speed
Collisions create resistance to flow of
charge
Resistance
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Due to collisions of conduction electrons
with atoms
Unit is ohm (W); 1 ohm = 1V/1A
Circuit elements designed to provide
measured amounts of resistance called
resistors
Resistance Laws
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Resistance of uniform conductor directly
proportional to its length, inversely
proportional to its cross sectional area
Resistance increases when temperature
increases for most metals
Resistance depends on nature of the
material: the resistivity (rho) has units
of ohm cm; R = r l/A
Range of Resistivities
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Low resistivity materials called
conductors; most metals
High resistivity materials called
insulators; nonmetals
In between are semiconductors: Si, Ge,
B, Se; can act as conductors or
insulators under certain circumstances
Resistance and Temperature
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Most conductors have a wide temperature
range where resistance is constant—called
ohmic because they obey Ohm’s Law
(I=V/R)
Resistance increases at high
temperature—light bulbs are non-ohmic
Resistance of many semiconductors varies
directly with temp.—digital thermometers
Superconductivity
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Discovered by Onnes (1908) while
investigating low temp conductivity
Resistance drops suddenly to zero at
critical temperature
Critical temp for most materials is a few
kelvins, but newer composite materials
found with superconductivity at higher
temperatures
Superconductivity
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Practical uses include MRI machines,
levitating, high speed trains, research
Electric Shock
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Current causes injury, not voltage
Currents can be high if skin conductivity
is high -- wet or salty
Must be a potential difference for
current to flow -- connection to high
voltage not dangerous unless path to
ground exists
Grounded (3 wire) and polarized plugs
help prevent shocks
Direct and Alternating Current
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DC: direct current, flow of charge in
one direction only – batteries
AC: alternating current, electrons
vibrate back and forth; don’t actually
flow through circuit
In USA, current alternates between
+120 V to -120V at 60 Hz
AC can be transmitted for long
distances with little loss due to heat
Converting AC to DC
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Often need DC for electronic devices
(stereos, computers, TV, etc.)
Diode acts as one way valve turning AC
into pulsed DC
2 or more diodes together can provide
smoother DC
Capacitors also used to smooth out DC
signal
EMF
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For continuous current, need sustained
potential difference and closed
conducting path or circuit
Work must be done on charges to
maintain potential difference; called
emf
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Unit: volt; symbol: script E
Ohm’s Law
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Circuit current is determined by emf of source
and resistance in circuit.
E where E is source emf, I is
I
RT source current and RT is total
resistance in circuit
Internal resistance of battery must be
included in total resistance
V = IR gives voltage drop across any
resistance element in circuit
Energy of Electric Current
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Emf source does work on electrons
Electrons then do work on circuit
components: resistors, bulbs, motors,
etc.
One coulomb of charge moved through
potential difference of one volt equals
one joule of work done, energy increase
also 1J
Energy of Electric Current
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W = qV = VIt (since q = It)
For one electron moved through 1 volt,
unit of work/energy is electron volt (eV)
1 eV = 1.60 x 10-19 J
Energy and Resistance
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Work done on resistance by current appears
as heat; can be desirable (oven, iron,
heater) or not (motor, light, computer)
Since resistance always present in normal
circuits, some energy lost due to heat
Joule’s Law: Q = I2Rt
Use to calculate heat produced by
resistance and current over a time period
Power in Electric Circuits
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Since power is work or energy
transferred/time, P = VI
For a resistive element, P = I2R power
dissipated in a resistance
If current is not known, P = V2/R
For total power in circuit, use E of emf
source for V and RT of circuit for R
Power Companies
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Energy sold in kilowatt-hours, a unit of
energy (power x time)
1 kW-hr means device used 1000 watts
of power for one hour
To minimize power loss in transmission
lines, high voltages and fairly low
currents used
345
kV
345,000V
138,000V
138 kV
24 kV
25,000V
5000V
240V
12 kV
Emf sources
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Electromagnetic: generator - creates
emf through electromagnetic induction
Photoelectric: solar cell or photoelectric
cell - uses photoelectric effect
Thermoelectric: thermocouple temperature difference in dissimilar
metals in contact produces potential
difference
Emf Sources
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Piezoelectric: crystalline material which
creates potential difference when
distorted by pressure - used in
microphones, acoustic instrument
pickups, igniters
Chemical: battery - uses chemical
reaction to transfer charges from one
electrode to another
Battery Cells
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Wet cells: use liquid electrolyte - car battery
Dry cells: use paste “dry” electrolyte flashlight batteries
Primary cells: replaced when reactants are
used up
Storage cells: easily recharged
Fuel cells: New reactants added as needed
Combinations of Cells
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Battery is combination of cells connected in
series, parallel, or combination of both
Cells in series: cells connected + to -, as in a
flashlight
battery emf = sum of cell emf’s; battery
current = current of one cell, the same
throughout; battery resistance = sum of cell
resistances
Combinations of Cells
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Cells in parallel: - terminals all
connected together and + terminals all
connected together
Battery emf = emf of one cell; total
current drawn by circuit is divided
equally among the cells; battery
resistance is reciprocal of the sum of
reciprocals of cell resistances
Electric Circuit
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An electric circuit has three parts:
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A source of emf (battery, generator, etc.)
a closed conducting path
a device to use the energy provided by the
battery—called the load
A short circuit is when no load is present or
is bypassed in some way producing high
currents
Simple Circuit
can be modeled by a pump to simulate a battery and a
paddle to simulate electrical resistance.
As the current turns the paddle it does work and thus
loses some energy similar to electrical current flowing
through a resistor.
Series Circuits
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Only one path for circuit current
Current the same in all parts of circuit
Sum of voltage drops across circuit
elements equals source emf
Total circuit resistance equals sum of
separate resistances
Series Circuit
Parallel Circuits
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More than one conducting path for circuit
current
Two or more components connected
across two common points in circuit
Currents in parallel branches vary
inversely with branch resistance; total
current = sum of branch currents
Parallel Circuits
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Voltage drop the same across parallel
branches
Parallel resistances add following
reciprocal rule: reciprocal of total
resistance equals sum of reciprocals of
individual resistances
Adding Parallel Resistances
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For two parallel resistors
R1 R2
Req 
R1  R2
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For two or more parallel resistors
1
1
1
1
 
  ...
Req R1 R2 R3
Parallel Circuit
Home Electrical Circuits
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Circuits in homes are in parallel; devices
are connected in parallel
When many resistances connected in
parallel, total resistance is low, current
high
Too much current through wires causes
excessive heating, fire hazard
Circuits protected from high currents by
circuit breakers or fuses
Circuit Networks
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Combination of series and parallel
To analyze, first find total resistance
(RT), then total current
To simplify resistance networks, replace
several resistances with one equivalent
resistance(Req)
Start with series resistances and
combine
Circuit Networks
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Then collapse parallel branches into one
equivalent resistance
Combine series resistances created by
previous step
Continue until only one equivalent
resistance remains
Complex Circuit
Kirchhoff’s Rules
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Algebraic sum of currents at any circuit
junction equals zero; or currents into a
junction equal currents leaving the
junction; conservation of charge
Algebraic sum of all voltage drops and
voltage gains around a circuit loop
equals zero; conservation of energy
Electrical Measurements
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Voltmeter must be placed in parallel
with circuit element whose voltage drop
is being measured
Ammeter must be placed in series so
that all circuit current flows through
ammeter.
Never connect the ammeter in
parallel like the voltmeter
Measuring Resistance
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Resistance can be measured using a
voltmeter and ammeter and calculating
resistance using Ohm’s Law
Some error is introduced by the meters
Multimeter uses this method
Wheatstone bridge gives more precise
measurement
Wheatstone Bridge
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Compares a ratio of a known resistance
to an unknown resistance with the
resistance of two lengths of high
resistance wire.
Uses sensitive current detecting device
called a galvanometer
l1/l2 = Rx/R when no current is detected
by galvanometer
Wheatstone Bridge Circuit