Series and Parallel Circuits Kirchoff

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Series and Parallel CircuitsKirchoffs Voltage
and Current Laws

• Circuits 1
• Fall 2005
• Harding University
• Jonathan White

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Outline

• Node definition
• KCL
• The current entering a node is equal to the
  current leaving a node.
• KVL
• The sum of voltages around a closed loop is 0.
• Series circuits
• Resistors in series add
• Req is always greater than R1 and R2
• Voltage Dividers
• Parallel circuits
• Resistors in parallel follow the equation Req
  (R1R2)/(R1R2).
• Req is always less than R1 and R2

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Nodes

• A node is where 2 or more elements meet.
• For now, and element can be a resistor, a voltage
  source, or a current source.
• Each point in the node must be electrically the
  same.
• Exp

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Kirchoffs Current Law

• A fundamental law of nature, like the Law of
  Conservation of Mass.
• KCL is the conservation of charge charge can
  neither be created or destroyed.
• KCL definition The sum of all currents entering
  a node is equal to the sum of all currents
  leaving the node.
• KCL holds for every node in a network and it
  works at every point in time.

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KCL

• Write equations for the current in each of the
  nodes in the circuit below

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Kirchoffs Voltage Law

• A fundamental law of nature, like the Law of
  Conservation of Energy.
• KVL is the conservation of electrical energy
  electrical energy can neither be created or
  destroyed, only transferred.

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KVL 2

• As the charge moves from the top of the battery
  to the top of Element 1 (along the wire shown in
  purple), how much energy does the charge lose?
• As the charge moves from the top of Element 1
  through Element 1 to the bottom of element 1,
  how much energy does the charge lose?
• As the charge moves from the bottom of Element 1
  to the top of Element 2, how much energy does
  the charge lose?
• As the charge moves from the top of Element 2
  through Element 2 to the bottom of element 2,
  how much energy does the charge lose?
• As the charge moves from the bottom of Element 2
  to the bottom of the battery, how much energy
  does the charge lose?
• As the charge moves from the bottom of the
  battery through the battery to the top of the
  battery, how much energy does the charge lose?

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KVL - 3

• What is Vb equal to?
• KVL definition the sum of voltages around a
  closed loop is 0.

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KVL - 4

• Write all the KVL equations for the circuit below

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Series Resistance

• 2 devices are said to be in series when the same
  current physically flows through both.
• Current flows into one element, through the
  element, out of the element into the other
  element, through the second element and out of
  the second element.  No part of the current that
  flows through one resistor "escapes" and none is
  added. 
• You see series resistance everyday

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Series Resistance - 2

• Consider the simplest series resistance
• What is Vs ?
• The equivalent resistance for resistors in series
  is always the sum of the individual resistors.

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Voltage Dividers

• Used as volume controls in electronic devices
• Provides a continuous sound spectrum, i.e., not
  digital.
• Used in RC combinations to filter out input noise
  in devices such as tachometers and
• A voltage divider looks like this

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Voltage Dividers - 2

• How much current flows through Ra and Rb ? Use
  Ohms Law.
• What is Vout ?
• As Rb goes to 0, whats the value of Vout ? Rb is
  then physically like what?
• As Rb goes to 8, whats the value of Vout ? Rb is
  then physically like what?

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Parallel Resistors

• 2 resistors are in parallel if the same physical
  voltage appears across each resistor.
• Each resistor provides its own path for the flow
  of current. If the resistors have different
  resistance values, they will carry different
  amounts of current, each in accordance with Ohm's
  Law.

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Parallel Resistors - 2

• Consider the simplest parallel resistance to the
  right. What is Ip?
• In parallel resistors, the equivalent resistance
  is always lower than either of the resistors.