Download Chapter 5 – Series Circuits

Chapter 5 – Series dc Circuits
Introductory Circuit Analysis
Robert L. Boylestad
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
Introduction
 If a wire is an ideal conductor, the potential
difference (V) across the resistor will equal the
applied voltage of the battery.
 V (volts) = E (volts)
 Current is limited only by the resistor (R). The
higher the resistance, the less the current.
5.2 - Series Resistors
The total resistance of a series
configuration is the sum of the resistance
levels.
RT  R1  R2  R3  R4  ...  RN
 The more resistors we add in series, the
greater the resistance (no matter what
their value).
Series Resistors
 When series resistors have the same value,
RT  NR
Where N = the number of resistors in the string.
 The total series resistance is not affected by the order
in which the components are connected.
5.3 – Series Circuits
 Total resistance (RT) is all the
source “sees.”
 Once RT is known, the current
drawn from the source can be
determined using Ohm’s law:
E
Is 
RT
 Since E is fixed, the magnitude of
the source current will be totally
dependent on the magnitude of RT .
Series Circuits
 The polarity of the voltage across a resistor is
determined by the direction of the current.
V1  IR1
V2  IR2
V3  IR3
 When measuring voltage, start with a scale that will
ensure that the reading is lower than the maximum
value of the scale. Then work your way down until a
reading with the highest level of precision is made.
5.4 – Power Distribution in a Series
Circuit
The power applied by the dc supply must equal that
dissipated by the resistive elements.
PE  PR1  PR2  ...  PRN
5.5 - Voltage Sources in Series
 Voltage sources can be connected in series to
increase or decrease the total voltage applied to
the system.
 Net voltage is determined by summing the
sources having the same polarity and subtracting
the total of the sources having the opposite
polarity.
5.6 - Kirchhoff’s Voltage Law

Kirchhoff’s voltage law (KVL) states that the
algebraic sum of the potential rises and drops around
a closed loop (or path) is zero.
Kirchhoff’s Voltage Law
 The applied voltage of a series circuit equals the sum of
the voltage drops across the series elements:
V
rises
 Vdrops
The sum of the rises around a closed loop must equal the sum
of the drops.
 The application of Kirchhoff’s voltage law need not
follow a path that includes current-carrying elements.
 When applying Kirchhoff’s 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.
5.7 – Voltage Division in a Series Circuit
 The voltage across the resistive elements will divide
as the magnitude of the resistance levels.
 The greater the value of a resistor in a series circuit, the
more of the applied voltage it will capture.
Voltage Divider Rule (VDR)
The VDR permits determining the voltage levels of a circuit
without first finding the current.
E
VX  R X
RT
Voltage Division in a Series Circuit
 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.
5.8 - 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 5.19
Insert Fig 5.20
5.9 - Notation
Voltage sources and grounds
Ground symbol
Voltage source symbol
Notation
Double-subscript notation
 Because voltage is an “across” variable and exists between
two points, the double-subscript notation defines 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
point (b).
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 .
Notation
 General Relationship
 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 – V b
5.10 – Voltage Regulation and the Internal
Resistance of Voltage Sources
 The ideal voltage source has no internal resistance
and an output voltage of E volts with no load or full load.
 Every practical voltage source (generator, battery, or
laboratory supply) has some internal resistance.
 Voltage across the internal resistance lowers the source
output voltage when a load is connected.
 For any chosen interval of voltage or current, the
magnitude of the internal resistance is given by
Rint = VL / IL
Voltage Regulation and the Internal Resistance of
Voltage Sources
 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 (VR) characteristics are measures of
how closely a supply will come to maintaining a supply
voltage between the limits of full-load and no-load
conditions.
Voltage Regulation and the Internal
Resistance of Voltage Sources
 Ideal conditions: VFL = VNL and VR = 0%
 The lower the voltage regulation, the less the
variation in terminal voltage with changes in
load
VNL  VFL
VR 
100%
VFL
5.11 – Loading Effects of Instruments
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

Loading Effects of Instruments
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

5.13 – 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.
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
ensure 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.
Applications
A Series Alarm Circuit