Chapter 5

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Chapter 5 Series Circuits

• Introductory Circuit Analysis
• Robert L. Boylestad

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5.1 - Introduction

• Two types of current are readily available,
  direct current (dc) and sinusoidal alternating
  current (ac)
• We will first consider direct current (dc)

Insert Fig 5.1
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Introduction

• If a wire were an conductor (no opposition to
  flow), the potential difference V across the
  resistor will equal the applied voltage of the
  battery
• V (volts) E (volts)
• Current then is limited only by the resistor (R)
  The higher the resistance, the less the current

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5.2 - Series Circuits

• Two elements are in series if
• They have only one terminal in common
• The common point between the two elements is not
  connected to another current-carrying element
• If all elements in the circuit are in series,
  then the network is called a series circuit
• Examples of a series circuit are the tying of
  small pieces of rope together to form a longer
  rope and the connecting of pipes to get water
  from one point to another

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Series Circuits

• Current is the same through series elements
• Used to determine if two elements are in series
• A branch of a circuit is any portion of the
  circuit that has one or more elements in series
• The total resistance of a series circuit is the
  sum of the resistance levels
• RT R1 R2 R3 R4 . RN

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Series Circuits

• Total resistance (RT) is all the source sees
• Once RT is known, the current drawn from the
  source can be determined using Ohms law
• Since E is fixed, the magnitude of the source
  current will be totally dependent on the
  magnitude of RT

Insert Fig 5.5
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Series Circuits

• The fact that current is the same through each
  element of a series circuit permits a direct
  calculation of the voltage across each resistor
  using Ohms law
• V1 IR1, V2 IR2, V3 IR3, VN IRN
• The total power delivered to a resistive circuit
  is equal to the total power dissipated by the
  resistive elements
• Pdel P1 P2 P3 PN

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5.3 - Voltage Sources in Series

• Voltage source can be connected in series to
  increase or decrease the total voltage applied to
  the system
• Net voltage is determined by summing the sources
  with the same polarity and subtracting the total
  of the sources with the opposite pressure
• ET E2 E3 - E1 (assuming that E1 has a
  different polarity than E2 and E3 )

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5.4 - Kirchhoffs Voltage Law

• Kirchhoffs voltage law (KVL) states that the
  algebraic sum of the potential rises and drops
  around a closed loop (or path) is zero

Insert Fig. 5.12
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Kirchhoffs Voltage Law

• The applied voltage of a series circuit equals
  the sum of the voltage drops across the series
  elements
• ? Vrises ? Vdrops
• (the sum of the rise around a closed loop must
  equal the sum of the drop)
• The application of Kirchhoffs voltage law need
  not follow a path that includes current-carrying
  elements
• When applying Kirchhoffs voltage law, be sure
  to concentrate on the polarities of the voltage
  rise or drop rather than on the type of element
• Do not treat a voltage drop across a resistive
  element differently from a voltage drop across a
  source

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5.5 - Interchanging Series Elements

• Elements of a series circuit can be interchanged
  without affecting the total resistance, current,
  or power to each element
• In the Figures below, resistors 2 and 3 are
  interchanged without affecting the total
  resistance

Insert Fig 5.20
Insert Fig 5.19
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5.6 - Voltage Divider Rule

• The voltage across the resistive elements will
  divide as the magnitude of the resistance levels
• It is the ratio of resistor value that counts
  when it comes to voltage division and not the
  relative magnitude of all the resistors
• Voltage Divider Rule (VDR)
• Permits determining the voltage levels of a
  circuit without first finding the current

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Voltage Divider Rule

• The voltage across a resistor in a series
  circuit is equal to the value of the resistor
  times the total impressed voltage across the
  series elements divided by the total resistance
  of the series elements
• The rule can be extended to voltage across two
  or more series elements if the resistance
  includes total resistance of the series elements
  that the voltage is to be found across

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5.7 - Notation

• Voltage sources and grounds
• Ground symbol with its defined potential
• Symbol for voltage source

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Notation

• Double-subscript notation
• Because voltage is an across variable and
  exists between two points, the double-subscript
  notation define differences in potential
• The double-subscript notation Vab specifies
  point a as the higher potential. If this is not
  the case, a negative sign must be associated with
  the magnitude of Vab
• The voltage Vab is the voltage at point a with
  respect to (w.r.t.) point b

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Notation

• Single-subscript notation
• The single-subscript notation Va specifies the
  voltage at point a with respect to ground (zero
  volts). If the voltage is less than zero volts,
  a negative sign must be associated with the
  magnitude of Va

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Notation

• General comments
• If the voltage at points a and b are known with
  respect to ground, then the voltage Vab can be
  determined using the following equation
• Vab Va - Vb

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5.8 - Internal Resistance of Voltage Sources

• Every source of voltage (generator, battery, or
  laboratory supply) has some internal resistance
• The ideal voltage source has no internal
  resistance and an output voltage of E volts with
  no load or full load
• Internal voltage across the internal resistance
  is computed using the formula Vint IFLRint
• For any chosen interval of voltage or current,
  the magnitude of the internal resistance is given
  by
• Rint ?VE / ?IL

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5.9 - Voltage Regulation

• For any supply, ideal conditions dictate that
  for a range of load demand (IL), the terminal
  voltage remains fixed in magnitude
• If a supply is set at 12 V, it is desirable that
  it maintain this terminal voltage, even though
  the current demand on the supply may vary
• Voltage regulation characteristics (VR) are
  measures of how closely a supply will come to
  maintaining a supply voltage between the limits
  of full-load and no-load conditions

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Voltage Regulation

• Ideal conditions, VFL VNL and VR 0
• The smaller the voltage regulation, the less the
  variation in terminal voltage with change in load
  
• VR (Rint / RL) X 100

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5.10 - Measurement Techniques

• For an up-scale (analog meter) or positive
  (digital meter) reading an ammeter must be
  connected with current entering the positive
  terminal and leaving the negative terminal
• Ammeters are placed in series with the branch in
  which the current is to be measured

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Measurement Techniques

• Voltmeters are always hooked up across the
  element for which the voltage is to be determined
• For a double-script notation Always hook up the
  red lead to the first subscript and the black
  lead to the second.
• For a single-subscript notation Hook up the red
  lead to the point of interest and the black lead
  to the ground

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5.11 - Applications

• Holiday lights
• Holiday lights are connected in series if one
  wire enters and leaves the casing
• If one of the filaments burns out or is broken,
  all of the lights go out unless a fuse link is
  used
• A fuse link is a soft conducting metal with a
  coating on it that breaks down if the bulb burn
  out, causing the bulb to be by-passed, thus only
  one bulb goes out.

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Applications

• Microwave oven
• A series circuit can be very useful in the
  design of safety equipment
• In a microwave, it is very dangerous if the oven
  door is not closed or sealed properly. Microwaves
  use a series circuit with magnetic switches on
  the door to insure that the door is properly
  closed.
• Magnetic switches are switches where the magnet
  draws a magnetic conducting bar between two
  conductors to complete the circuit.

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Applications

• Series alarm circuits