Physics 272
February 12
Spring 2015
www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm
go.hawaii.edu/KO
Prof. Philip von Doetinchem
philipvd@hawaii.edu
PHYS272 - Spring 15 - von Doetinchem - 267
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:
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Flashlights
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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
https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc
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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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Light bulbs in series and parallel
http://www.youtube.com/watch?v=apHkG4T6QHM
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What makes a classic light bulb glow is the
dissipation of energy in the filament:
If current to light bulb is reduced (for what ever reason) by a factor
of 2. The dissipated energy becomes smaller by a factor of 22
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Light bulbs in series and parallel
Current and power in each light bulb:
Voltage is the same for both light bulbs
Current and power in each light bulb:
The current per light bulb is half with respect to
parallel connection. Also the potential drop over
each light bulb is half as it is split between both
light bulbs.
Less power dissipation per light bulb in series connection with the same power source.
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Equivalent resistance
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An infinite network
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An infinite network
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An infinite network
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Rules to calculate currents in more
complicated networks
Definitions:
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Junction: three or more conductors
meet
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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:
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Junction: three or more conductors
meet
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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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