Resistance

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Resistance

• Electrical Systems

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Electrical Resistance

• Opposition to the flow of electrons
• Collisions between electrons and atoms
• Electrons drift velocity is very low because of
  all the collisions

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Resistivity

• When we studied fluid resistance we learned that
  a longer thinner pipe had more resistance to
  fluid flow
• The resistance of a wire is affected by
• Length of wire (longer wiregreater resistance)
• Diameter of wire (smaller diameter greater
  resistance)
• Wire material
• R ? (L/A)

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Resistivity of Materials
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Resistance in a Circuit

• Resistance is calculated using Ohms law
• The potential difference (voltage) across an
  ideal conductor is proportional to the current
  through it.
• The constant of proportionality is called the
  resistance, R
• Ohm's Law is given by
• V I R
• Units for Resistance
• Ohms (?)
• Equal to 1 Volt/Amp

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Ohms Law

• An electrical device with a resistance of 100 ?
  has a current of 30 mA flowing through it. What
  is the potential difference of the voltage
  source?
• V IR
• V (3 mA) x (100 ?)
• V (0.030 A) x (100 ?)
• V 3 V

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Ohms Law

• When connected to a 120-V source, an electric
  heater will allow 10 Amps of current to flow.
  What is the resistance of the heater?
• V IR
• R V / I
• R 120 V / 10 A 12 ?

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Schematic Diagrams

• Symbols for circuit elements

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Resistors in Series

• Only one path for charge to take
• Current is the same in each
• One resistor burns out, it opens the circuit and
  charge can no longer flow
• All the lights go out (

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Potential Drop in Series

• As a charge goes through a resistor, its
  potential (voltage) drops
• The charges leave the battery with potential that
  drops through each resistor depending on the
  resistance
• Potential drops to zero when it reaches the
  opposite terminal

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Equivalent Resistance Series

• One resistor that could replace all the resistors
  in the circuit
• REq is always larger than the biggest resistor
• As each charge has to go through each resistor in
  series, the total resistance is found by adding
  them all up.
• REq R1 R2 R3 ...

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Example Problem Series

• Find the equivalent resistance
• Use Ohms Law to find the total current
• Current is the same in all resistors
• Find the voltage drop across each one using Ohms
  Law

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Resistors in Parallel

• Each resistor added in parallel provides
  another path for current to flow
• If one light burns out, the rest can stay on
  because all the other lights still have a
  complete loop connected to the battery

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Potential Drop in Parallel

• Because each resistor is connected to the
  battery, the voltage across each one is the same
• The voltage across each resistor is equal to the
  potential difference of the battery

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Equivalent Resistance Parallel

• When more paths are added, resistance goes down
• REq is always less than the smallest resistor!

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Equivalent Resistance Parallel

• If the resistors are equal, two resistors will
  cause half as much resistance and 3 resistors
  will cause one-third as much resistance
• Instead of adding
• 1/REq 1/R1 1/R2 1/R3

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Example Problem Parallel

• Find the equivalent resistance
• Find the total current using Ohms Law
• The voltage is the same for all resistors
• Find the current in each resistor using Ohms Law

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Combination Circuits

• Circuits can sometimes be a combination of both
  series and parallel resistors
• Find the equivalent resistance for the parallel
  resistors
• Add this to the series resistors

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Example Problem Combination Circuit

• Find the resistance in the following circuit
• Parallel 1/REq (1/6?) (1/6?) 2/6?
• REq 6 ? /2 3 ?
• Series REq 3 ? 3 ? 5 ? 11 ?

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Series vs. Parallel

• Resistors are like toll booths on a highway

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Series vs. Parallel

• Series Circuits
• The current is the same in every resistor this
  current is equal to that from the battery.
• IT I1 I2 I3
• The sum of the voltage drops across each resistor
  is equal to the voltage of the battery.
• VT V1 V2 V3
• The equivalent resistance of the collection of
  resistors is greater than any one resistor and is
  found by the equation
• REq R1 R2 R3 ...

• Parallel Circuits
• The voltage drop is the same across each parallel
  branch and is equal to that in the battery.
• VT V1 V2 V3
• The sum of the current in each individual branch
  is equal to the total current from the battery.
• IT I1 I2 I3
• The equivalent resistance of the collection of
  resistors is smaller than any one resistor and is
  found by the equation
• 1/REq 1/R1 1/R2 1/R3 ...

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Applications of Electrical Resistance

• When you need control the flow of current
• Control the amount of electrical energy used by a
  device
• Convert electrical energy into heat, light,
  sound, motion, and information
• Clipart http//www.physicsclassroom.com/