14 February 2002 Electric Circuits - Princeton...
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14 Feb 2002 Physics 102 Lecture 2 1 Electric Circuits Physics 102 Lecture 2 14 February 2002 HAPPY VALENTINE’S DAY
Transcript of 14 February 2002 Electric Circuits - Princeton...
14 Feb 2002 Physics 102 Lecture 2 1
Electric Circuits
Physics 102
Lecture 2
14 February 2002
HAPPY
VALENTINE’S
DAY
14 Feb 2002 Physics 102 Lecture 2 2
LAURA HELLER - WEDNESDAY LAB
14 Feb 2002 Physics 102 Lecture 2 3
CapacitorsTwo parallel conducting plates with equal but
opposite charges form a capacitor.
Neglecting “fringing” near the edges: The field inside is uniform with (σ is the charge per unit area on the plate q/a)
The field outside vanishes.
The charge on each plate of a capacitor isproportional to the potential differencebetween the plates, .
Capacitance has units farad=coulomb/volt.For this geometry , sohas units of farads/meter.
Capacitors store energy
E ==σ ε/ 0
q CV==
C A d==ε0 / ε0
d
A
CVQ C
====
2
22
2/
/
14 Feb 2002 Physics 102 Lecture 2 4
Capacitors and Dielectrics
A dielectric material in a capacitorwill reduce the field strength by afactor (dielectric constant).
The voltage is also reducedbecause . Since , C must
increase when the dielectric isinserted.
For parallel plates: C A d= κε 0 /
κ = E E0 /
V Ed=q CV const= = .
14 Feb 2002 Physics 102 Lecture 2 5
Energy in Capacitor with Dielectric
Without a dielectric:C V Q
C== ==0 0
20
2
02 2
With a dielectric:C V Q
C== ==0 0
202
02 2κ κIf we charge up a capacitor with a dielectricnearby, what will happen?
A) Nothing, dielectrics are electrically neutral.
B)The dielectric is repelled.
C)The dielectric is sucked in.
14 Feb 2002 Physics 102 Lecture 2 6
A dielectric is inserted between the platesof a capacitor. The system is then chargedand the dielectric is removed. The electrostaticenergy stored in the capacitor is
A. greater thanB. the same asC. smaller than
it would have been if the dielectric were leftin place.
14 Feb 2002 Physics 102 Lecture 2 7
A parallel-plate capacitor is attached to abattery that maintains a constant potentialdifference V between the plates. While thebattery is still connected, a glass slab is insertedso as to just fill the space between theplates. The stored energy
A. increases.B. decreases.C. remains the same.
14 Feb 2002 Physics 102 Lecture 2 8
Electromotive Force and Currents
� Chemical reactions cantransfer charge from oneplace to another
� Charge separation createsan electrical potentialdifference, or emf(electromotive force)
� Sustained emf creates acurrent in a conductingwire:[unit of currentampere=coulomb/second]
Biochemical 1-100 mV
Dry cell battery 1.5 V
Auto battery 12 V
Van de Graaff 4.5 MV
Lightning 108-109 V
I q t= ∆ ∆/Potential DIFFERENCES
14 Feb 2002 Physics 102 Lecture 2 9
Voltage Vs. Current
The voltage is the energy per charge.In a fluid analogy, voltage is like a pressure difference.
Batteries produce voltage differences. Pumps, forexample, produce pressure differences.
Current is the number ofcharges through a crosssection per second.
Current corresponds to theflow of water in the fluidanalogy.
Pressure differencefrom height ofreservoir correspondsto voltage.
Waterreservoir
Av I→∆ ∆P V→
14 Feb 2002 Physics 102 Lecture 2 10
Ohm’s LawIn many materials, the current that flowsis proportional to the voltage across(potential difference) the material: I V∝The proportionality constant is the resistanceR, a property of the particular piece ofmaterial
Ohm’s Law: V IR=
Note that Ohm’s “Law” is only an approximation that holds trueover a particular range of currents and voltages, and it is not atall correct for some materials; it is not a fundamental law.
∆VI
14 Feb 2002 Physics 102 Lecture 2 11
Series and Parallel Circuits
� When multiple resistors are connected in a circuit,we use two simple rules:
�Resistors in series
�Resistors in parallel
R R R= +1 2
1 1 1
1 2R R R= +
�More complex circuits are broken into simple pieces
i
14 Feb 2002 Physics 102 Lecture 2 12
Resistive Properties of Materials
� Resistivity is an intrinsic property of a material
� L is length of object
� A is cross sectional area of objectFFFFF� ρ is the resistivity (units ohms·meters)
� Resistivity (and resistance) often depend ontemperature (increasing with T in metals)
RL
A= ρ
ρ ρ αα
= + −= + −
0 0
0 0
1
1
[ ( )]
[ ( )]
T T
R R T T Cool
14 Feb 2002 Physics 102 Lecture 2 13
•Recall that power is energyper unit time.
•As charges move (or currentsflow), the electric field doeswork on the particles (changestheir energies).
•Recall that a watt is the SIpower unit, so kilowatt-hour isa unit of energy.
PEt
qVt
IV= = =∆∆
∆∆
= =I IR I R( ) 2
=
=V
RV
VR
2
14 Feb 2002 Physics 102 Lecture 2 14
•The resistance of circuit I is smaller than of circuit II•Hence more current flows through battery in I•P=IV, hence power is greater in circuit I
A. I
B. They’re the same
C. II
14 Feb 2002 Physics 102 Lecture 2 15
AC Circuits
� Outlets supply 120V 60 Hz “AC” (alternatingcurrent) which is generated by a local power plant.
� There are three wires a)a ground [green], b)a neutral[white], and c) a HOT wire [black].
� Why do we get power from an alternating current?
14 Feb 2002 Physics 102 Lecture 2 16
RC Circuits
� Circuits with bothcapacitors and resistorshave time variable currents
q q e
V V e
I I e
t RC
t RC
t RC
== −−
== −−
==
−−
−−
−−
0
0
0
1
1
( )
( )
/
/
/
14 Feb 2002 Physics 102 Lecture 2 17
RC Puzzler
This is called a “relaxation oscillator.”
Why does the light blink?
