Test Review Chapters 2528

1
Test Review Chapters 25-28

• PHYS 2326-15

2
Test Coverage

• Primarily on what topics covered in class since
  last test
• Can include questions or parts based upon prior
  classes or courses
• Responsible for the material in the chapters
  covered

3
Test Tips

• Show the problem set up graphically if possible
• Show equations to use
• Provide intermediate steps to solution
• Show solution and intermediate values
• Make your 3x5 formula card carefully, include
  your constants

4
Important Concepts

• Electric Work
• Electric Potential Energy
• Electric Potential
• Potential Difference
• Scalar Fields
• Vector Fields
• Gradient
• Potential Gradient

5
Electric Work
6
Uniform Electric Field
7
Point Charges
8
Important concepts

• Volt Joule/Coulomb
• Electric Field is
• 1Newton / Coulomb 1 Volt / meter
• Work is Force x distance moved and is the change
  in energy Joules

9
ExampleUniform field between 2 plates

• Chap 25.1 example
• In uniform field, eqn 25.6 applies
• E(Vb-Va)/d
• Given 2 sheets separated by 0.3cm with 12 volt
  battery applying a voltage across them.

10
Example 2

• E(12)/0.003 4.0E3 V/m
• NOTE Consistancy with units is KEY

11
Concepts to Know

• Capacitors
• Capacitance
• Energy Density
• Dielectric
• Dielectric Constant
• Permittivity
• Series and Parallel Circuits

12
Capacitance

• Capacitance is the ability for an object to hold
  a charge for a given potential energy
• C Q/?V
• C is the capacitance in Farads
• that can hold a charge Q with an increase in
  potential of ?V volts.
• 1 Farad 1 coulomb of charge per Volt
• This is a huge value

13
Parallel Plate Capacitor

• most common type of component although most are
  rolled up or contain many plates
• C eo A/d
• Capacitance is proportional to area /inverse
  proportional to separation

14
Dielectrics

• When nonconducting material is inserted in a
  capacitor, in between the plates the voltage
  drops.
• That means since CQ/V that C increases
• C ?Co
• e ? eo permittivity of free space
• The electric field is E Eo/? s/?eo between 2
  plane sheets

15
Capacitor Circuits

• 2 capacitors in parallel ?V is the same and the
  total charge is the sum of each
• C C1 C2 .
• 2 capacitors in series Q is the same and ?V is
  the sum of the individual ?Vs.
• 1/C 1/C1 1/C2
• Parallel Series

16
Solving for Equivalents

• Reduce the number of real capacitors down to
  equivalent capacitors, combining simple parallel
  and series combinations

C6
C1
C2
C5
a
c
a
a
C3

C3
b

C4
b
b
a
C4

C4
C7
b
17
Example 1

• 4 capacitors arranged in previous slide
• potential is 10V above ground for a, ground for
  b. Find a) voltage and charge on each capacitor
  b) find voltage on pt c wrt ground.
• C1 12nF, C2 24nF, C3 22nF, C415nf

18
Example 1

• C1 and C2 in series combine to a C5 1/C5
  1/C1 1/C2 8 nF
• C3 and C5 are parallel combine to C6 C6 C5
  C3 30nF
• C6 and C4 are series combine to C7 1/C7 1/C6
  1/C5 10nF
• V for C7 10V, QCV (10nF)(10) 100nC

19
Example 1

• A) V7 V Q7 C7V7 Q7 100nC
• Q6 Q7 Q6 C6V6 V6 3.33V
• Q4Q7 Q4C4V4 V46.667V
• V3 V6 Q3C3V3 Q3 73.33nC
• V5 V6 Q5C5V5 Q526.67nC
• Q2Q5 Q2C2V2 V21.111V
• Q1Q5 Q1C1V1 V12.22V
• b) VcV2V4

20
Example 2

• A parallel plate capacitor made from 2 squares of
  metal, 2mm thick and 20cm on a side separated by
  1mm with 1000V between them
• Find
• a) capacitance b)charge per plate c) charge
  density d)electric field e) energy stored f)
  energy density

21
Example 2

• Given
• L 20cm 0.2m
• d 1mm 1E-3m
• V 1E3 V
• epsilon 8.85E-12 F/m
• Equations
• Ceo A/d, AL2 , QCV, s Q/A, V-Ed, U1/2
  QV, u U/Ad 1/2 eo E2

22
Example 2

• a) C eo A/d (8.85E-12)(0.2)2/(1E-3) 0.354nF
• b) QCV (0.354nF)(1E3V) 0.354 µC
• c) s Q/A (0.354 µC)/(0.04 m2 ) 8.85E-6 C/
  m2
• d) VEd, E V/d 1000/0.001 1.0E6 V/m (this
  is a magnitude)
• e) U (1/2)(0.354E-6)(1000)1.77E-4J
• f) u (1/2)(8.85E-12)(1.0E6) 2 4.425J/m3

23
Capacitance Review

• Capacitance C Q/?V
• Parallel plate capacitor C eo A/d
• Energy U ½ QV ½ C V2 Q2 /2C
• Energy density u ½ eo E2
• Dielectric (dialectric constant)
• C ?Co
• e ? eo
• E Eo/? s/?eo

24
Capacitance Review

• Circuits Series and Parallel
• Parallel capacitance adds since V the same,
  qcv, cq/v
• Series 1/Ct 1/C1 1/C2 .
• q is constant C1V1 C2V2
• 1/C1 V1/q, 1/C2 V2/q, 1/C3V3/q
• 1/Ct V1/q V2/q V/q
• 1/C 1/C1 1/C2 .

25
Concepts to Know

• Current
• Drift Velocity
• Concentration of Particles
• Current Density
• Resistivity
• Resistance
• Temperature Coefficient of Resistivity
• Electric Power

26
Ohms Law

• ?V (l / s) J (l / (s A) ) I R I
• R ?V/I
• R resistance Ohm (O) 1 Volt/Ampere
• s conductivity 1/? (rho) resistivity
• R ? (l / A)
• bulk property increases with length, decreases
  with cross sectional area
• resistivity function of material and of
  temperature

27
Resistance Temperature Coefficient

• Resistivity
• ? ? o (1 a (T-To ) )
• a (alpha) is temperature coefficient of
  resistivity
• Since resistance is proportional to resistivity
• RRo (1 a (T-To ) )

Resistance schematic symbol
28
Electrical Power

• Power dissipation in a resistor
• dU/dt d/dt (Q?V) dQ/dt ?V I ?V
• U energy, I current
• Power P delivered to resistor I ?V
• Often E symbol used for V so we have PIE
• Using Ohms law IV/R
• P I2 R (?V) 2/R
• Power is Watts Joules / second

29
Resistance Circuits

• I ?V/R ?V Va-Vb
• Parallel Series
• 1/R I/?V R ?Vx/I
• I I1 I2 I3 ?V ?V1?V2?V3

Vb
Va
Va
Vb
Parallel Series 1/Rt 1/R1 1/R2 1/R3
Rt R1R2R3
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Example 3

• Combine Series R1 R2 toR5
• Combine Parallel 1/R5 1/R4 1/R6
• Combine Series R6 R3 R7

R2
R6
c
R1
a
Ro
R4
Ro
R3
R5
R3
b
R4
Ro
R7
R3
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Example 3

• Given Ro 1 O, R1 1O, R2 2 O, R3 3 O
• R4 6 O, Vo 12V Find a) voltage across and
  current through each resistor, b) voltage Vab
  across the battery, c) the electric potential at
  point c.
• Find equivalent resistance and work backwards to
  get voltage and current

32
Example 3

• R5 R1R2 12 3 O
• R4 R5 parallel 1/R6 1/R4 1/R5 2 O
• Ro, R6 R3 in series, R7 RoR6R3 6 O
• V IR7, IV/R 2A
• Io I3 I6 I
• Vo IoRo 2 V
• V3 I3 R3 6V
• V6 I6 R6 4V
• V5 V6 I5 R5, I5 1.333A
• V4 V6 I4 R4, I4 0.667A
• I2 I5, V2I2 R2, V2 2.667V

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Example 3

• a) Vo 2 V Io 2 A
• V1 1.333 V I1 1.333 A
• V2 2.667 V I2 1.333 A
• V3 6 V I3 2 A
• V4 4V I4 0.667A
• b) Vab V Vo 10V
• c) Vc Vcb V2V3 8.667V

34
Concepts to Know

• ElectroMotiveForce EMF
• Junction
• Loop
• dArsonval Galvanometer
• Ammeter
• Voltmeter
• Ohmmeter
• Potentiometer
• Multimeter

35
Electromotive Force - EMF

• e electromotive force a force that creates a
  charge such as the chemical reaction in a battery
  which builds up a voltage potential.
• ?V e Ir where I is the current and r is the
  internal resistance of the battery or device.
• I e/(R r)

36
Load Matching

• See example 28.2
• Net result maximum power is transferred when the
  load resistance R r internal resistance.

37
Ohms Law Review

• I V/R, V IR, R V/I
• Power Watts Joules /sec
• P IV I2 R V2/R
• Series Resistances add
• Parallel Resistances 1/Rt 1/R1 1/R2
• opposite from capacitors

38
Kirchoffs Rules

• Junction Rule at any junction (3 or more
  connections) the sum of all currents 0
• there can be no charge buildup at the junction
• Loop Rule The sum of the potential differences
  across all elements around a closed loop must 0

39
Potential Difference across a component

• Going around the loop mark a plus by the end of a
  component on the side where the assigned current
  is coming from. Going with the current flow a
  resistor drops voltage a battery increases going
  to which is going downstream. Going against
  the assigned current flow a resistor increases V
  and a battery decreases from to -.

40
Example 1 Kirchoffs Rules

• R1 1O, R2 1 O, R3 3 O, R4 4 O,
• R5 5 O, R6 6 O

R4
R2
b
d
a
R3
10V

R1
R5

5V
c
R6
41
Example 1

• Assign currents for the loops
• Determine resistor high V sides for these
  currents and place signs

I2
10V
I1




I3

42
Example 1

• Set up equations for the 3 loops
• -1O I1 - 2 O I2 - 3O I1 3O I2 5V 0
• 3 O I1 - 3 O I2 - 4 O I2 10V - 5 O I2 5 O I3
• -5V 5 O I2 - 5 O I3 - 6 O I3
• Rearrange
• 6 I1 3I2 0 I3 5 V/ O 5 A
• -3 I1 12 I2 5 I3 10 A
• 0 I1 5 I2 11 I3 -5A

43
Solve by determinants

• Make determinant for equations, denominator first
  then solve for each I column

44
Solving for Currents
45

• Repeating for the final current I3

46
dArsonval galvanometer

• Standard analog meter, typical might have 10 ohms
  and full scale current of 1ma
• If low resistance shunt across it becomes an
  ammeter
• If resistor added in series reads voltage

47
Example 2

• Given dArsonval galvanometer with 10 Ohms and
  full scale reading at 1ma
• find a) min. voltage for F.S., b)shunt needed for
  ammeter F.S. 0.1A, c) Series resistance needed
  for voltmeter at 20V F.S. and d) what voltage is
  read at one-quarter full scale

48
Example 2

• Rg 10 O, current at F.S. 0.001 A
• Va IR 0.001 10 0.010V or 10mV
• for shunt in parallel with meter R and total
  current Ib, Va Ib Rb, where 1/Rb 1/Rs 1/Rg,
  Rb0.1 O, Rs 0.10101 O
• Vc IgRc, Rc RgRs, Rc 20K O
• Rs 19.99k O
• d) ¼ full scale 20/4 5V

49
RC Circuits

• I Io exp(-t/RC) RC time constant tau
• I dq/dt
• I e/R
• See section 28.4
• See example 28.10 for energy in capacitor at time
  t is
• UQ2/(2C)exp(-2t/RC)
• falls off twice as fast