Physics II

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Physics II

• Simple DC Circuitry

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Todays Quote (wishful thinking)

• Atomic power will make electricity too cheap to
  meter
• Glenn Seaborg

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Todays Cartoon
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Todays BrainBoggler
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Todays Vocabulary Word

• pixilated \PIK-suh-lay-tud\ 

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And pixilated means

• adjective 1 somewhat unbalanced mentally
  also bemused2 whimsical

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DC vs. AC

• DC Direct Current
• Seat of emf always drives current in same
  direction (indicated by same algebraic sign)
• May vary in magnitude, however.
• AC Alternating Current
• Seat of emf drives current (usually periodically)
  in oscillating directions
• Amplitude must vary

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Circuit elements for DC

• Seat of emf such as battery or DC power supply
• Switches
• Single pole-single throw
• Double pole-double throw
• Resistors (sometimes referred to as load)
• Motors
• Lamps
• Radio/TV/computer circuitry
• A myriad of others
• Connecting wires (hook-up wire, leads) with very
  low (usually regarded as zero) resistance
• No voltage drops occur across hook-up wires
• Each point on an unbroken segment of hookup wire
  is at same potential

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Terminology

• Potential drop voltage drop
• Difference in energy per unit positive charge
  from one end of an element to the other.
• Voltages are across elements, not through them
• Current passes through elements.
• Power
• Rate of energy generation in seat of emf
• Rate of energy dissipation in resistances
• Terminal voltage of seat of emf
• V E Ir

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Basic Rules for very simple circuits

• Ohms Law applies to each resistive element
• V IR
• Voltage drops, together with seat of emf,
  conserve energy
• At junctions (3 or more wires meet) current in
  equals current outno charge build-up

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Series arrangement

• For seats of emf
• --- connections
• Emfs add algebraically
• For resistors
• Same current flows in each resistor in a series
  branch.
• Conventional current flows from to end of
  resistor--downhill
• Electrons flow opposite way-uphill
• Ammeters always in series with elements

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Equivalent resistance (series)

• Rate of generation
• Pgen EI
• Measured in Watts (1 W 1 J / 1 s)
• Power dissipated in one resistor
• Pdis VI I2R V2/R
• Power dissipated in series combination
• Pdis V1I V2I V3I Vn I
• I (IR1 IR2 IR3 IRn) (factor Ohm)
• Current is same in all resistors in series
  (definition)
• To conserve energy
• Pgen Pdis .

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Equivalent series resistance

• From conservation of energy
• Pgen Pdis .
• Determine what 1 resistance would produce same
  dissipation power
• Pdis I2 Rs I2 (R1 R2 R3 Rn)
• Pgen EI
• Thus
• Rs R1 R2 R3 Rn .

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Parallel arrangement

• Seats of emf
• Connected , - -
• Same emf as any one of them
• Larger current capacity
• Resistors
• Same potential difference across parallel
  branches (whether emf or from other circuit
  elements as in voltage divider)by definition
• Voltmeters always in parallel with element

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Still must conserve energy

• Pgen EI
• At branch current divides
• More current flows through smallest resistance
  branch
• I (I1 I2 I3 In )
• But same voltage drop across all
• Pdis V1I1 V2I2 V3I3 Vn In
• In parallel branch all voltage drops are equal
• Pdis V(I1 I2 I3 In )
• V2/R1 V2/R2 V2/R3 V2/Rn
• V2 x (1/R1 1/R2 1/R3 1/Rn )
• Pgen Pdis .

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Parallel Equivalent Resistance

• Determine what one resistor will produce same
  power dissipation rate as does the parallel
  branch
• Pdis V2 x (1/R1 1/R2 1/R3 1/Rn )
• V2/ Rp V2 x (1/R1 1/R2 1/R3 1/Rn )
• 1 / Rp 1/R1 1/R2 1/R3 1/Rn
• Reciprocal of resistance is conductance
• G 1 / R
• Measured in mho or Siemen

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Two parallel resistors

• Rp R1R2 / (R1 R2 )
• R1 /R2 I2 / I1 .
• More generally for a k resistance parallel branch
• RjIj RmIm
• Where i, m are no larger than k.

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Voltage Divider circuit

• Seat of emf in series with two resistors
• Load in parallel with one of the two resistors
• Voltage divider provides a smaller voltage to
  load than would the seat of emf.
• Voltage across load voltage drop across which
  resistor is in parallel.

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Voltage Divider Details

• I2 E / (R1 R2RL /(R2 RL))
• V2 I2R2 ILRL VL
• This is potential drop across load
• IL ER2 /(RL (R1 R2RL /(R2 RL)))
• This is the load current

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