Physics 272
February 13
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
philipvd@hawaii.edu
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Summary
current
current density
resistance
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Summary
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Ideal source of emf brings charge to higher potential
energy level without increasing the kinetic energy
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Energy and power in electric circuits
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How fast is energy delivered or extracted?
If a charge passes through a circuit element: change of
potential energy
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Current stays the same → no gain of kinetic energy
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Power:
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Power for a pure resistance:
Phys272 - Spring 14 - von Doetinchem - 282
Power
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Moving charges collide with atoms in resistor
→ increase internal energy of material (energy dissipation)
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Maximum power rating of resistors before it overheats
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Power output:
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Power input:
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Source with larger emf pushes current backward through source with lower
emf (charging of car battery with alternator)
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Power
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Charging a rechargeable battery:
–
Electric energy is transformed to chemical energy
–
Battery gets warm from dissipated energy
Strategy for solving circuit problems:
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Draw circuit
–
Identify elements: sources of emf, resistors, capacitors,
(inductors)
–
Target variables
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Source of emf delivers (takes) power when current flows from –
to + (+ to -)
–
Resistor: always positive power input → removes energy from
the circuit
–
Important check: energy conservation
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Power
Ir2
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Increasing resistance reduces power input to resistor
(50W light bulb has larger resistance than 100W light bulb)
Shorted circuit (R=0):
–
No net power output
–
dissipates all energy within the source: quickly ruins battery
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Theory of metallic conduction
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Classic model, no quantum effects for electrons
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each metal atom donates one electron
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Freely moving electrons
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Stationary ions
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Electrons follow straight lines without electric fields
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Random directions
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Electric field causes to bend electron tracks
–
Electrons are slowed down in collisions
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Theory of metallic conduction
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Theory of metallic conduction
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Tolman-Stewart experiment
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How do we know that the free charges in a metal
are negative?
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Abruptly stop a rapidly spinning spool of wire and
measure the potential difference between the ends of the
wire
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Simplified version: accelerate a metal rod uniformly
–
Charges lag behind rod motion → electric field builds up
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Tolman-Stewart experiment
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Review
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Current is the amount of charge flowing through a specified area
per unit time
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Current is a scalar and current density a vector
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Current is defined in direction of the flow of positive charges
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Resistivity of a good conductor is small
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Ohm's law works for many materials and describes the resistivity
as being independent of the electric field
Potential difference and current are directly proportional with
resistance as proportionality constant.
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Complete circuit needs a continuous current carrying path
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Steady current must come from a source of emf
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Circuit elements can put energy into a circuit or can take it out
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Discussion
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Batteries are always labeled with their emf; for instance, an AA flashlight battery is
labeled 1.5V. Would it be appropriate to put a label on the batteries stating how much
current they provide?
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No, current depends on the total resistance of the circuit connected across the battery terminal
–
current depends not only on the battery but also on the rest of the circuit.
Current causes the temperature of a real resistor to increase. Why? What effect does
the heating have on the resistance?
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resistor converts electrical energy to thermal energy → increases temperature
–
depends on how the resistivity of the resistor depends on the temperature
–
If the resistor is metallic its resistance will increase. If the resistor is made of a semiconductor its
resistance will decrease.
Long distance, electric power, transmission lines always operate at very high voltage,
sometimes as much as 750kV. What are the advantages of such high voltages? What
are the disadvantages?
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Power input to a device: P =VI
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Larger V means smaller I
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Energy loss in the wires occurs at a rate I2R
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Smaller I = less energy loss
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Disadvantage: danger of high voltages, step up and step down the voltage before and after
transmission.
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Direct-current circuits
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Study networks
of circuit elements:
find voltages and
currents
Important: charge
conservation
Direct current:
currents are not
changing:
–
Flashlights
–
Automobile wiring
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Resistors in series and parallel
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Combinations of resistors play an important role in many
devices
Series and parallel connection:
What are the currents?
(similar to the question with capacitors → charges)
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Series: currents are the same
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Parallel: potential differences are the same
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Similar to capacitors: equivalent resistance
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Resistors in series
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Voltages are directly proportional to resistance and
current
The equivalent resistance of any number of
resistors in series equals the sum of their individual
resistances
Equivalent resistance is greater than any individual
resistance
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Resistors in parallel
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Current is proportional to common voltages, but inversely
proportional to the resistance
For any number of resistors in parallel, the reciprocal of the
equivalent resistance equals the sum of the reciprocals of
their individual resistances.
The equivalent resistance is always lower than any individual
resistance.
More current goes through the path of least of resistance.
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Resistors in series and parallel
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Network of resistors can be replaced by an
individual one
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Make a drawing
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Identify groups of series and parallel connections
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Target variables: equivalent resistance, potential
differences, currents
Series: potential differences add up, current is the
same
Parallel: potential difference is the same, currents
add up
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Equivalent resistance
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Rules to calculate currents in more
complicated networks
Definitions:
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Junction: three or more conductors
meet
–
Loop: any closed path in a circuit
Kirchhoff's junction rule:
Source: http://de.wikipedia.org/wiki/Gustav_Robert_Kirchhoff
Kirchhoff's rules
Gustav Kirchhoff
(1824-1887)
Algebraic sum of
currents is zero at
any junction.
Conservation of charge
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Definitions:
–
Junction: three or more conductors
meet
–
Loop: any closed path in a circuit
Kirchhoff's loop rule:
Source: http://de.wikipedia.org/wiki/Gustav_Robert_Kirchhoff
Kirchhoff's rules
Gustav Kirchhoff
(1824-1887)
Algebraic sum of potential differences is zero in any
loop.
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Electrostatic force is conservative. Path does not
matter → potential energy is the same after going
around a loop
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Kirchhoff's rules
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Draw circuit diagram
Indicate directions of currents and emf (use junction
rule)
Chose direction for loops, has to the same as the
current direction:
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Add potential differences and set to zero
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Sign convention:
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Emf: - → + positive, + → - negative
Resistor:
–
–
travel opposite to current direction → positive
travel in current direction → negative
–
Do that for other loops
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Solve set of equations
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Charging a battery
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