Physics 272
October 2
Fall 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_fall_272_uhm.html
Prof. Philip von Doetinchem
philipvd@hawaii.edu
Phys272 - Fall 14 - von Doetinchem - 1
Review
●
Current is the amount of charge flowing through a specified
area per unit time
●
Current is a scalar and current density a vector
●
Current is defined in direction of the flow of positive charges
●
Resistivity of a good conductor is small
●
●
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.
●
Complete circuit needs a continuous current carrying path
●
Steady current must come from a source of emf
●
Circuit elements can put energy into a circuit or can take it
out
Phys272 - Fall 14 - von Doetinchem - 2
Energy and power in electric circuits
●
●
How fast is energy delivered or extracted?
If a charge passes through a circuit element: change of
potential energy
●
Current stays the same → no gain of kinetic energy
●
Power:
●
Power for a pure resistance:
Phys272 - Fall 14 - von Doetinchem - 3
Power
●
Moving charges collide with atoms in resistor
→ increase internal energy of material (energy dissipation)
●
Maximum power rating of resistors before it overheats
●
Power output:
●
●
Power input:
Direction does not
matter for a resistor →
energy is dissipated in
any case
Source with larger emf pushes current backward through source with lower emf
(charging of car battery with alternator)
Phys272 - Fall 14 - von Doetinchem - 4
Power
2
2
I r=4A 2=8W
I2r
●
●
Increasing external resistance reduces power input to
resistor
Shorted circuit (R=0):
–
No net power output
–
dissipates all energy within the source: quickly ruins battery
Phys272 - Fall 14 - von Doetinchem - 5
Direct-current circuits
●
●
●
Study networks
of circuit elements:
find voltages and
currents
Important: charge
conservation
Direct current:
currents are not
changing:
–
Flashlights
–
Automobile wiring
Phys272 - Fall 14 - von Doetinchem - 8
Resistors in series and parallel
●
●
●
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)
●
Series: currents are the same
●
Parallel: potential differences are the same
●
Similar to capacitors: equivalent resistance
Phys272 - Fall 14 - von Doetinchem - 9
Resistors in series
●
●
●
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
Phys272 - Fall 14 - von Doetinchem - 10
Resistors in parallel
●
●
●
●
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.
Phys272 - Fall 14 - von Doetinchem - 11
Resistors in series and parallel
●
Network of resistors can be replaced by an
individual one
●
Make a drawing
●
Identify groups of series and parallel connections
●
●
●
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
Phys272 - Fall 14 - von Doetinchem - 12
Equivalent resistance
Phys272 - Fall 14 - von Doetinchem - 13
Light bulbs in series and parallel
http://www.youtube.com/watch?v=apHkG4T6QHM
●
●
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
Phys272 - Fall 14 - von Doetinchem - 15
An infinite network
Phys272 - Fall 14 - von Doetinchem - 20
An infinite network
Phys272 - Fall 14 - von Doetinchem - 21
An infinite network
Phys272 - Fall 14 - von Doetinchem - 22
●
●
●
Rules to calculate currents in more
complicated networks
Definitions:
–
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
Phys272 - Fall 14 - von Doetinchem - 23
●
●
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.
●
Electrostatic force is conservative. Path does not
matter → potential energy is the same after going
around a loop
Phys272 - Fall 14 - von Doetinchem - 24
Kirchhoff's rules
●
●
●
Draw circuit diagram
Indicate directions of currents and emf (use junction
rule)
Chose direction for loops
–
Add potential differences and set to zero
–
Sign convention:
●
●
Emf: - → + positive, + → - negative
Resistor:
–
–
travel opposite to current direction → positive
travel in current direction → negative
–
Do that for other loops
–
Solve set of equations
Phys272 - Fall 14 - von Doetinchem - 25