Download Chapter 5 – Series Circuits

Chapter 5 – Series 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 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

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
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
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
I s= R
T


Since E is fixed, the magnitude of the
source current will be totally dependent
on the magnitude of RT
Insert Fig 5.5
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 Ohm’s 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
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 )

5.4 - 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
Insert Fig. 5.12
Kirchhoff’s 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 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

5.5 - 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 5.19
Insert Fig 5.20
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

xE
Vx = RR
T
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
5.7 - Notation

Voltage sources and
grounds


Ground symbol with its
defined potential
Symbol for voltage source
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
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 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
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 = DVE / DIL
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

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%
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

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

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.
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.
Applications

Series alarm circuits