Chapter 26 Capacitance wrap up

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Chapter 26 Capacitancewrap up

• PHYS 2326-11

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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

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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 .

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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

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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

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Example 2

• a) C eo A/d (8.85E-12)(0.2 m)2/(1E-3 V)
  0.354nF
• b) QCV (0.354nF)(1E3 V) 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-4 J
• f) u (1/2)(8.85E-12)(1.0E6)2 4.425 J/m3

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Chapter 27 Ohms Law

• PHYS 2326-12

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Concepts to Know

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

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Current

• Current is I dQ/dt Amperes A C/s
• Coulombs per second Amps Amperes
• This is charge passing through a point or surface
  during time t
• Uses positive charge for CONVENTIONAL current
  flow (Same as electrons moving in opposite
  direction)

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Drift Velocity

• Microscopic model of charge is the flow of charge
  carriers.
• See Example 27.1 for drift speed of electrons
  very very slow like 0.223 mm per second for
  actual current flow
• The electric field/voltage changes etc. is almost
  the speed of light.

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Current Density

• Current density is the current per unit area
  traveling through a cross sectional area A.
• J I/A Amperes/meter squared
• Valid for cross section perpendicular to the
  direction of travel and for uniform current
  density.
• J s E where sigma is the conductivity of the
  conducting material (not valid for all materials)
  For those where valid Ohms Law

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Ohms Law

• Jn q vd where n is the free electrons/m3 , vd
  is the drift velocity and q is the charge per
  electron,
• I n q vd A where A is the cross sectional area
  perpendicular to the current flow
• V El when a small V is applied between the ends
  of a wire of length l
• J sE sV/l
• sigma is conductivity not charge density

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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

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Resistors

• Resistors are components designed to have a
  particular value. Typically, these have a color
  code with value and multipliers. BBROYGBVGW is
  0-9 or 1,10,100, . 109, Gold silver none are
  5, 10 and 20 for the old ones. Standard
  values are a bit odd as theyre based upon
  accuracy ranges. Modern ones are typically 5 2
  1 or better

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Resistor Types

• Carbon film most common now
• Carbon composition becoming rare but is best
  under surge conditions like nearby lightning
• Other common types wire wound, precision metal
  film
• Platinum RTD (resistance temperature devices) are
  very high precision temperature measurement
  sensors.

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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
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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