Series Circuits

1
Chapter 5

• Series Circuits

2
Series Circuits

• Two elements are said to be in series if they are
  connected at a single point and if there are no
  other connections at this point.
• A series circuit is constructed by connecting
  various elements in series.
• Current will leave the positive terminal of a
  voltage source, move through the resistors, and
  return to the negative terminal of the source.

3
Series Circuits

• Current flowing through a circuit is similar to
  water flowing through a pipe - current leaving
  the element must be the same as the current
  entering the element.
• The identical current occurs everywhere in a
  circuit.
• The laws, theorems, and rules that you apply to
  DC circuits also apply to AC circuits.

4
Kirchhoffs Voltage Law

• The summation of voltage rises and voltage drops
  around a closed loop is equal to zero.
• E - V1 - V2 - V3 0
• Another way of stating KVL is The summation of
  voltage rises is equal to the summation of
  voltage drops around a closed loop.
• V1 V2 V3 E

5
Resistors in Series

• Almost all complicated circuits can be
  simplified.
• For a series circuit,
• V1 V2 V3 E
• IR1 IR2 IR3 E
• I(R1 R2 R3 ) E
• I(R1 R2 R3 ) I(Rtotal)
• The total resistance in a series circuit is the
  sum of the resistors.

6
Power in a Series Circuit

• The power dissipated by each resistor is
  determined by the power formulas
• P VI V2/R I2R
• Since energy must be conserved, the power
  delivered by the voltage source is equal to the
  total power dissipated by all the resistors.
• PT P1 P2 P3

7
Voltage Sources in Series

• In a circuit with more than one source in series,
  the sources can be replaced by a single source
  having a value that is the sum or difference of
  the individual sources.
• Polarities must be taken into account.
• The resultant source will be the sum of the rises
  in one direction minus the sum of the voltages in
  the opposite direction.

8
Interchanging Series Components

• The order of series components may be changed
  without affecting the operation of the circuit.
• After circuits have been redrawn, it becomes
  easier to visualize the circuit operation.

9
The Voltage Divider Rule

• The voltage applied to a series circuit will be
  dropped across all the resistors in proportion to
  the magnitude of the individual resistors.
• The total voltage dropped across the resistors
  must equal the applied voltage sources by KVL.

10
Voltage Divider Rule

• If a single resistor is very large compared to
  the other series resistors, then the voltage
  across that resistor will be essentially the
  source voltage.
• If the resistor is very small, then the voltage
  will be essentially zero.
• If a resistor is more than 100 times larger than
  another resistor, then the smaller resistor can
  be neglected.

11
Circuit Ground

• Ground is a point of reference or a common point
  in a circuit.
• One type of grounding is chassis ground.
• In this type of grounding, the common point of
  the circuit is often the metal chassis of the
  piece of equipment.

12
Circuit Ground

• Chassis ground is often connected to Earth
  Ground.
• Earth ground is physically connected to the earth
  by a metal pipe or rod.
• If a fault occurs within a circuit, the current
  is redirected to the earth.
• Voltages are often made with respect to ground.

13
Double Subscripts

• If we wish to express the voltage between two
  points a and b, we can express this as Vab.
• If a is at a higher potential than b, then the
  voltage is positive if b is at a higher
  potential, the voltage is negative.

14
Double Subscripts

• To determine correct polarity, first calculate
  all voltage drops across all components.
• Assign polarities.
• As you go around a circuit, add the gains and
  subtract the drops.

15
Single Subscripts

• In a circuit with a reference point, most
  voltages are expressed with respect to that
  reference point.
• The voltage at point a with respect to ground is
  Va.
• Any voltage with a single subscript is with
  respect to ground.

16
Single Subscripts

• If the voltages at various points in a circuit
  are known with respect to ground, then the
  voltage between points is easily determined.
• Vab Va - Vb

17
Point Sources

• A voltage source that is given with respect to
  ground may be represented by a point source.
• The points represent voltages with respect to
  ground, even if ground is not shown.
• Point sources simplify the representation of a
  circuit.

18
Internal Resistance of Voltage Sources

• Ideal sources have no internal resistance.
• In an ideal source, the terminal voltage does not
  change when the load changes.
• For a practical source, there is internal
  resistance.
• As the load changes, the drop across the internal
  resistance changes, and the terminal voltage
  changes.

19
Ammeter Loading Effects

• An ammeter is placed in a circuit to make a
  measurement its resistance will affect the
  circuit.
• The amount of loading is dependent upon the
  instrument and the circuit.
• If the resistance of the meter is small compared
  to the resistance of the circuit, the loading
  effect will be small.