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PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Lecture 10
Chapter 26
Capacitorsin Series and Parallel
Physics II
Is there life before coffee?Hmm! 8am Physics class triggers
philosophical questions
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Today we are going to discuss:
Chapter 26:
Section 26.5
Oncethebatteryisdisconnected,Q hastoremain
constant,sincenochargecanfloweithertoor
fromthebattery.
Aparallel‐platecapacitorinitiallyhasapotentialdifferenceof400V andisthendisconnectedfromthechargingbattery.Iftheplatespacingisnowdoubled,whatisthenewvalueofthevoltage?
A)100V
B)200V
C)400V
D)800V
E)1600V
+Q –Q
ConcepTest Varying Capacitance II
Since,whenthespacingd isdoubled,
thecapacitanceC ishalved.Andsince ,thatmeansthevoltagemustdouble
400 VQ =CΔV≝
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Combinations of Capacitors
In practice, two or more capacitors are sometimes joined together. The circuit diagrams below illustrate two basic combinations:
parallel capacitors and series capacitors.
The equivalent capacitance is the capacitance of the single capacitor that can replace a set of connected capacitors without changing the operation of the circuit
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Capacitors in ParallelConsiderthreecapacitorsconnectedinparallel.
QReal
circ
uit
Equi
vale
nt c
ircui
t
ΔV
, ΔV
, ΔV
, ΔV
Q ΔV
Ceq
Capacitors in parallel have the same potential difference, ΔV
Qisatotalchargedrawnfromthebattery+ +
Since ≝;;;
Wehavereplaced3capacitorswitha“equivalent”capacitor.
+ +
+ +
Conservationofcharge
Ceq isinsertedwithoutchangingtheoperationofthecircuit,soQandΔVaresameasintherealcircuit
Equivalentcapacitanceofcapacitorsinparallel.
= =
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
+ +
Capacitors in SeriesConsiderthreecapacitorsconnectedinseries.
QReal
circ
uit
Equi
vale
nt c
ircui
t
+Q
Q ΔV
Ceq
Capacitors in series have the same charge, Q.
+ +
Since ≝
Ceq isinsertedwithoutchangingtheoperationofthecircuit,soQandΔVaresameasintherealcircuit
Equivalentcapacitanceofcapacitorsinseries.
C1 C2 C3
+ -
-Q +Q -Q +Q -Q
ΔV
ΔV1 ΔV2 ΔV3
Q
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Lecture 11
Chapter 27
Current
Physics II
Is there life before coffee?Hmm! 8amPhysics class triggers
Philosophical questions
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Today we are going to discuss:
Chapter 27:
Section 27.1 Section 27.3-5
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
A Model of Conduction
Uptothispointweweretalkingaboutelectrostaticequilibriumwhenaconductorwasatthesamepotentialandtherewasnocurrent.
Nowifweaddabattery,apotentialdifferencewillbeimposedandtheelectronswillstarttravellingcreatingacurrent
Inthiscase,anelectronbouncesbackandforthbetweencollisions,butitsaveragevelocityiszero.
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Current (definition)
IfQisthetotalamountofchargethathasmovedpastapointinawire,wedefinethecurrentIinthewiretobetherateofchargeflow:
The SI unit for current is the coulomb per second, which is called the ampere.
1 ampere = 1 A = 1 C/s.
current is the rate at which charge flows
dQ
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Direction of current (convention)
Byconvention,currentisdefinedasflowingofmotionpositiveparticlesfrom+to‐.
Electronsactuallyflowintheoppositedirection.
Current (by convention motion of positive particles)
Current
Currentflowsfromapositiveterminalofabatterytoanegativeone.
.
Everyminute,120Cofchargeflowthroughthiscrosssectionofthewire.
A)240A
B)120A
C)60A
D)2A
E)Someothervalue
ConcepTest Current
Thewire’scurrentis
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
The Current Density in a Wire
Thecurrentdensity Jinawireisthecurrentpersquaremeterofcrosssection:
ThecurrentdensityhasunitsofA/m2.
A
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