Physics 272
February 18
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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Light bulbs in series and parallel
http://www.youtube.com/watch?v=apHkG4T6QHM
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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:
–
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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A complex network
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Ammeter
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Measure current that path through the meter
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Good Ammeter has a small internal resistance
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Voltmeters
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Voltmeters should have a large resistance such that
connecting them in parallel is not altering the
current of the circuit
Ammeter and Voltmeter in combination can
measure resistance and power
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R-C circuits
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So far: constant emfs and constant current
Next steps: time dependent potentials, currents, and
powers
What happens when you charge a capacitor?
many devices use charging and discharging
constantly:
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Flashing traffic lights
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Car turn signals
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Flash units
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Charging a capacitor
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Ideal battery (zero internal resistance)
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Capacitor initially uncharged
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Close switch → charge capacitor
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Assume:
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current starts at the
same time everywhere
in the circuit
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Current is the same
everywhere for a particular
moment in time
Lower case quantities are time dependent quantities
in the following calculations
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Charging a capacitor
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Capacitor charges:
–
vbc increases (charge builds up)
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vab decreases (Kirchhoff's loop rule)
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Current decreases (Ohm's law)
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Charging a capacitor
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Eventually:
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Capacitor fully charged
–
Current stops flowing
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Charging a capacitor
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Charge at any time t during the charging process:
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Charging a capacitor
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Current and time constant
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τ small: capacitor charges quickly
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τ large: capacitor charges slowly
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Charge and current processes happen on the same
time scale τ
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Charging a capacitor
Charge build-up
Current drop
q/Qf
i/I0
t
t
i/I0
Slope is -1/(RC)
→ measure properties
Logarithmic plot
t
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Discharging a capacitor
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Remove battery
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Time constant RC stays the same
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Charge goes exponentially to zero
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Power approach
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Energy conservation:
-Ri2
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Half of the energy is stored in capacitor. Other half is dissipated in resistor
(does not depend on C, R, ε)
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Example
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Power distribution systems
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Appliances at home are always operated in parallel
to the power source
Modern houses have two lines with opposite polarity
coming in (hot lines)
A third line is grounded and provides the neutral
potential
Maximum current is limited by resistance of the
wires (IR2 power loss)
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12 gauge wire (2.05mm → safe for 20A without
overheating)
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Thicker wires for, e.g.,main power lines, dryers
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Circuit overloads and short circuits
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Overload/overheat protection is provided by fuses
Fuses are designed to break circuits depending on the
maximum load allowed on the wires
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Installed on hot side of incoming line
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Fuse examples:
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lead-tin alloy with low melting temperature
→ melts when too hot
→ breaks circuit (one-time use)
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Electromagnet or bimetallic strip interrupts circuit (can be reset)
Short circuit: neutral and hot side are in contact
→ large current can melt wires!
3 prong connectors connect, e.g., metal housing to ground
line and can prevent shocks
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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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Review
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Resistors in series:
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Resistors in parallel:
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Kirchhoff's junction rule:
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Kichhoff's loop rule
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Discussion
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Why do the lights on a car become dimmer when the starter is operated?
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a large current is drawn from the battery by the starter motor and the terminal voltage of the
battery drops because of the voltage drop across its internal resistance.
In a two-cell flashlight, the batteries are usually connected in series. Why not
connect them in parallel? What possible advantage could there be in connecting
several identical batteries in parallel?
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in series the total voltage is the sum of the individual voltages
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in parallel the voltage across the bulb is just the voltage of a single battery
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in parallel the currents of the individual batteries add to give the total current, so more current
can be delivered by batteries in parallel
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if one battery goes dead the others still deliver current to the device and the voltage applied to
the device is unchanged
When a capacitor, battery, and a resistor are connected in series, does the resistor
affect the maximum charge stored on the capacitor? Why or why not? What purpose
does the resistor serve?
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capacitor fully charged: battery emf equals the voltage across the capacitor: Q =εC
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When charging is complete → no current through the resistor → resistor plays no role
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resistor affects the rate at which the capacitor charges
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