Physics 104: Lecture 4

1
Physics 104 Lecture 4

• Capacitance
• Parallel Series Capacitors
• Current
• Resistance
• Ohms Law
• Resistance vs. Temperature

2
From Before

• Electric force and field from charges. Vectors.

• Work done by an electric force and potential
  energy.

• Electric work and potential. Bring a charge from
  ? to r.
  Scalars.

3
Capacitance Parallel Plate Capacitor
V Q d/(e0A)
V
E

-
A
A
d
4
Dielectric

• Placing a dielectric between the plates increases
  the capacitance.
• C k C0

Dielectric constant (k gt 1)
Capacitance with dielectric
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Dielectric Constant, Strength

• How to achieve large energy storage - typically
  large C
• Small gap (d)
• Breakdown voltage is material dependent
• Large area (A)
• Would like to keep the device size tolerable
• Large dielectric constant (ke0)
• Large dielectric strength
• Dielectric constant/strength of material

( permittivity of a dielectric)
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Question?

• Consider a capacitor made of two parallel
  metallic plates separated by a distance d. A
  dielectric slab with thickness t is inserted
  between them without changing the charge on the
  original plates. The energy stored in the
  capacitor

1) increases 2) decreases 3) stays the same
Effective e increasesCeA/d increasesEcapQ2/2
C decreases However can typically store more
charge
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Capacitors in Parallel

• Both ends connected together by wire

Veq

• Same voltage V1 V2

• Add Areas Ceq C1C2
• Share Charge Qeq Q1Q2

15 V
15 V
15 V
C1
C2
V1
V2
Veq
10 V
10 V
10 V
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Capacitors in Series

• Same Charge Q1 Q2 Qeq
• Share VoltageV1 V2 Veq
• Add d

Q


C1
V1


-
Veq




C2
-Q
V2
-

-



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Electric Charges in a Circuit

• When the switch is closed, E-field is established
  (due to battery, V0)

• Electric wave moves down the wire to carry the
  signal

at the speed of light, 3 x 108 m/s!

• Free charges every where in the conductor begin
  to move

• Individual charges drift slowly (at Vd)

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Electric Current

• Whenever electric charges of like signs move, an
  electric current is said to exist
• The current is the rate at which the charge flows
  through across a surface such as the
  cross-section area of a wire
• The direction of the current is the direction
  positive charge would flow
• This is known as conventional current direction
• In a common conductor, such as copper, the
  current is due to the motion of the negatively
  charged electrons

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Current Resistance

• Current Rate at which charge flows
• Resistance That which impedes the free flow of
  charges - due to collisions in the material medium

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Drift Velocity

• Average velocity of free charges in a conductor
• Characteristic of the material

In a Cu conductor electrons drift Current is
defined to be in opposite direction.
Vd 0.4 mm/s - 1012 times slower than the signal
itself travels on a wire
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Electric Terminology

• Current Moving Charges
• Symbol I
• Unit Amp ? Coulomb/second
• Count number of charges which pass point/sec
• Power Energy/Time
• Symbol P
• Unit Watt ? Joule/second Volt Coulomb/sec
• PW/?tVq/?t VI

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Resistance

• In a conductor, the voltage applied across the
  ends of the conductor is proportional to the
  current through the conductor. ?VRI
• The constant of proportionality is the resistance
  of the conductor
• Units of resistance are ohms (?)
• 1 ? 1 V / A

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Physical Resistor

• Resistance Traveling through a resistor,
  electrons bump into things which slows them down.
  R r L /A
• r Resistivity Density of bumps
• L Length of resistor
• A Cross sectional area of resistor
• Ohms Law I V/R
• Double potential difference ?double current
• I (VA)/ (r L)

A
L
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Preflight 1

• Two cylindrical resistors are made from the same
  material. They are of equal length but one has
  twice the diameter of the other.
• R1 gt R2
• R1 R2
• R1 lt R2

2
1
Smaller diameter ? not as easy for stuff to flow
through
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Simple Circuit
I
V
R
I

• Example
• Calculate I when V24 Volts and R 8 W
• Ohms Law VIR
• I V / R 24 V / 8 W 3 A

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Ammeters Voltmeters

• Ammeters measure current
• In line with the bulb, all the charge passing
  through the bulb also must pass through the meter
• Voltmeters measure voltage (potential diff.)
• Connects to the two ends of the bulb

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Temperature Resistance

• For most metals, resistivity increases with
  increasing temperature
• With a higher temperature, the metals atoms
  vibrate with increasing amplitude electrons find
  it more difficult to pass through the atoms

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Resistance vs Temperature

• Resistance depends on
• Availability of free charges in material
• Collisions in the material medium
• Temperature dependence of resistance
• Number of free charges available in a material
  can depend on temperature
• Electrons can be freed from their orbits around
  nuclei
• The rate of collision of free charges with atoms
  depends on the temperature
• Higher the temperature the greater atomic
  vibration that increases collision probability

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Resistivity, Resistance vs. Temp.

• For most metals, resistivity increases
  approximately linearly with temperature over a
  limited temperature range
• ??? is the resistivity at some temperature T
• ???o is the resistivity at some reference
  temperature To
• To is usually taken to be 20 C
• ? is the temperature coefficient of resistivity
• Since the resistance of a conductor with uniform
  cross sectional area is proportional to the
  resistivity, you can find the effect of
  temperature on resistance

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Metals

• At room temperature metals have several free
  electrons per atom
• Resistivity varies with temperature linearly due
  to increasing probability of collisions with
  atoms

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Semiconductors

• At room temperature pure semiconductors have few
  free electrons
• With increasing temperature electrons are freed
  from atomic orbits
• Resistance decreases with temperature

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Super-conductors

• At very low temperatures resistance can drop to
  zero abruptly - phase transition

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Preflight 3

• An object is heated. Its resistivity
• always increases
• increases linearly with temperature
• stays the same
• decreases
• usually increases, but for some substances it can
  decrease

e.g., metals
e.g., stays same for manganin
e.g., semi-conductors
Most objects increase resistivity at higher temps
because the atoms vibrate more rapidly, creating
a greater collision of electrons. However, some
objects decrease resistivity with higher temps
because the temperature increases the number of
free charges available to carry current.
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Preflight 5

• As the light bulb ages, it gives off less light
  than when new. Why? (Mark all that apply)
• The resistivity of tungsten filament decreases
  with time
• The resistivity of tungsten filament increases
  with time
• The tungsten filament in the bulb is getting
  fatter as it collects crud on its surface with
  time.
• The tungsten filament in the bulb is getting
  thinner as its atoms are evaporating from it
  slowly with time.
• The bulb is accumulating coatings of dust from
  the environment on the outside and tungsten atoms
  from the tungsten filament on the inside. These
  cannot transmit light.