Chap.

5
 Two types of current
available to consumer today
Direct current (DC): ideally, the flow
of charge (current) does not change
in magnitude or direction with time.
Sinusoidal alternating current (AC):
the flow of charge is continually
changing in magnitude and direction
with time
 Basic concepts of an electric
circuit
Acircuit is a never-ending looped pathway
for electrons.

Any break in thiscircuitwill prevent

electrons from flowing through it:
The location of a break
Any discontinuity in in a circuit is irrelevant
thecircuitwill to its inability to
prevent electron sustain continuous
flow throughout the electron
entirecircuit. flow.Anybreak,anywh
erein a circuit prevents
electron flow
 Series DC Circuits

3 ways of connecting elements in a

circuit:
Series connection
Parallel connection
Any element not in series or parallel

http://www.tpub.com/neets/book1/chapter3/1-10.htm
Series configuration
 Series resistors
Fixed resistors have only two terminals to
connect in a configuration
When one end is connected to the end of
another device the resistors establish a
series connection
If three elements are connected to the
same point, none of the elements are in
series
The more
The total
resistors we add
resistance of a
in series, the
series
greater is the
configuration is
resistance, no
the sum of the
mater what their
 Resistors in series
Series configuration of resistors

Configuration in which none of the

resistors are in series
 Schematic of a series
connection of resistors
Connecting
resistors in series
increases the
resistance
between points a
&b
The total
resistance of a
Schematic = configuration
series
configuration is
the sum of the
resistance levels
The largest
resistor will
have the most
RT = R1 + R2 + R3 + R4+ RN impact to the
total resistance
 Breadboard, resistors in
series
When we wish to show that components
are connected to each other, we draw
their schematic symbols with lines
connecting the terminals together

Connected in series on a breadboard

 Resistors in Series
When all resistors
are the same
value, RT
equation can be
modified as
follow:
RT = NR
RT = R 1 + R + R
2 3 The total resistance
of resistors in series
= 10 + 30 + 100 is unaffected by the
order in which they
RT = 140 are connected
The more resistors we
add in a series
configuration, the
greater the resistance,
 Example 5.1
Determine the total resistance of the
series connection.

RT = R 1 + R 2 + R 3 + R 4
20 + 220 + 1.2k + 5.6k
RT = 7040 = 7.04k
 Example 5.2
Find the total resistance of the
Series resistors.

N is the number of resistors in series

of the same value
(4) (3.3k) = 13.2k

Go over example 5.3 on pg. 121

 Measuring the resistance
By connecting a Ohmmeter across the
access terminals.

It is important to realize
To use the multi-
meter as an that an
ohmmeter turn the ohmmetercannotbe
selector dial to used when the
point to the ohms resistance is connected
range
in a circuit and a
 instrumentation
The multimeter shown
can measure a range
of electrical quantities
including voltage (AC
or DC), ohms,
continuity,
capacitance, frequency
and current (AC or DC).
The rotary switch is used
to select the quantity (and
range) you wish to
measure.
 Measuring the resistance
Connect the test leads to
the sockets labeled 'COM'
and ''
To check the meter is working
touch the leads together and
the display should read0.0. It
may read slightly higher,
e.g.0.3. This is the resistance
of the test leads themselves.

Without anything connected

between the test leads the display
will give an out of range indication (-
1 in this case) to show that the
resistance is too large to
measure.
Using voltmeters to measure
the voltages across the
resistors
Voltages of a circuit
can be measured
without breaking the
circuit

When using a
voltmeter, start with
the scale that will
ensure that the
reading is less than
the max value of the
scale until you reach
the readings with the
highest level of
precision is obtained
 Measuring current

Using an ammeter to measure the

current of a circuit requires that the
circuit be broken at some point and
the meter inserted in series with
the branch in which the current is
to be determined
 Accuracy
The overall accuracy of the reading
will depend upon the multi-meter
model. The more expensive the
meter the better the accuracy will
be.
 Example 5.3
RT = R1 + R3 + NR2
4.7k + 2.2k + (3)(1k) = 9.9k
 What is a series circuit?
An electric circuit connected so that current
passes through each circuit element in
turn without branching. Series
Circuit

Circuit A circuit is any

combination of
element that will
result in a flow of
charge or current in
the configuration
 = 8.4v / 140
The direction of the
= 0.06 mA
conventional current is a
series dc circuit from the
negative to the positive
supply. It is leaving the
positive terminal and
returning to the negative
If current terminal
is the same for 2
The current is the same adjoining elements, the
at every point in a series elements may or may not
circuit be in series
 If any combination of two elements are in
series, the current must be the same, but
if the current is the same at two adjoining
elements, the elements may or may not
be in series.
 Polarity of voltage
Polarity of the voltage across a
resistor is determined by the
direction of the current.
Current entering a resistor creates a
drop in voltage

Reverse the Change the

direction of the orientation of the
current and the resistor, and the
polarity will same rules apply
reverse as in figure c
Magnitude of the voltage drop
Magnitude of the voltage drop across
each resistor can be found by
applying Ohms law using only the
resistance of each resistor
 Figure 5.12 pg 139
Current

= 8.4v / 140
= 60 mA

Magnitude of
voltage drop
across each
resistor
 Example 5.4
For the series circuit:
a)Find the total resistance
b)Calculate the resulting
current
c)Determine the voltage across each resistor
 Example 5.5 for the series
circuit:
a) Find the total resistance
b) Calculate the resulting
current
c) Determine the voltage
across each resistor
Elements can be rearranged
 Example 5.5 cont
b. Current is counterclockwise because
of the manner in which the dc power
was connected

c. The direction of the current will

define the polarity for V2
 Example 5.6
Given RT & I3, calculate R1 & E for the
circuit
RT = R1 + R2 + R3
Find R1

RT (R2 + R3)
= R1
 In-class problem

Calculate the voltage drop

Through each resistor
 In-class problem

Calculate the voltage drop

Through each resistor
Solution:
1st find RT, then total current (IT): 1+ 2+
3 = 6
IT = E / RT 24v / 6 = 4A
then find voltage across each resistor
 In-class problem
Calculate the voltage drop
Through each resistor
Solution:
1st find RT, then total current (IT): 1+ 2+
3 = 6
IT = E / RT 24v / 6 = 4A
then find voltage across each resistor
V1 = IT * RT = (1)(4A) = 4 v

V2 = IT * RT = (2)(4A) =8v
V3 = IT * RT = (3)(4A) =12 v
 Power distribution in a series
circuit
Power applied will be equal to the power
dissipated or absorbed. In other words,
the power applied by the dc supply must
equal that dissipated by the resistive
elements.
In a series configuration, maximum power
is delivered to the larges resistor
 Power distribution equations
Power applied by the dc
supply is equal to the
dissipated by the
resistive elements

Power delivered
by the supply

Power dissipated by
the resistive element
 Example 5.7
a) Determine total resistance RT
b) Calculate the current Is
c) Determine the voltage across each
resistor
 Example 5.7 cont
d) Find the power supplied by the battery
e) Determine the power dissipated
by each resistor
f) Does the power supplied equals
the total power dissipated?
5.5 Voltage sources in series
Voltage sources can be connected in
series to increase or decrease the total
voltage applied to a system.
The net voltage is determined by
adding the sources with the same
polarity and subtracting the total of the
sources with the opposite polarity.
The net polarity is the polarity with the
larger sum.
 Reducing series dc voltage
sources to a single source

In figure (a) sources will In figure (b) the greater the in

pressure current to follow a clockwise direction
clockwise path with the net voltage is
So the net voltage is ET = E1 + E2 - E3
ET = E1 + E2 + E3 = 9v + 3v - 4v = 8v
= 10v + 6v + 2v = 18v
 Is the same as
a 6v source

Four 1.5 v AAA

batteries
connected in
series to obtain a
source of 6v
Correct connection
The power available has increase by a for series dc
factor of 4 due to the increase in terminal supplies to
voltage establish a output
of 60v

Incorrect
connection
for series dc
supplies
 HW1
1 a &b, 3, 7, 9, 13, 17, 19
 Kirchhoffs Voltage Law (KVL)
Kirchhoff's Voltage Law - KVL - is one of
two fundamental laws in electrical
engineering
KVL is really conservation of electrical
energy.
It is the starting point for analysis of any
circuit.
KVL is like a loop
The application of the law require
Kirchhoffs voltage law

represents summation
The applied voltage the closed loop
of a series dc circuit
will equal the sum of V the potential drops &
the voltage drops of rises
the circuit
The sum of the
+ E V 1 V2 = 0
voltage rises around
a closed path will
always equal the sum
of the voltage drops
- E + V 1 + V2 = 0
E = V 1 + V2
How to write the KVL equation for
1. Pick a starting point on the loop you want to write KVL for.
2. Imagine walking around the loop - clockwise or
counterclockwise.
3. When you enter an element there will be a voltage
defined across that element. One end will be positive and
the other negative.
4. Pick the sign of the voltage definition on the end of the
element that you enter. You could also choose the sign of
the end you leave. (you have to be consistent all the way
around the loop)
5. Write down the voltage across the element using the sign
you got in the previous step.
6. Keep doing that until you have gone completely around
the loop returning to your starting point.
7. Set your result equal to zero.
 Write the KVL for each loop
Loop 1 .

Loop 2
Loop 3
For the first loop .
(Battery, Element
.
#1, Element #2)
-VB+ V2+ V1= 0
For the second loop
(Element #2, Element . .
#3, Element #4).
-V2+ V4- V3= 0
For the third loop (Battery,
There are only two Element #1, Element #3,
independent equations Element #4)
-VB+ V2+V1= 0 -VB+ V1- V3can
+V = 0
The third equation be4obtained
-V2+ V4- V3= 0 from the first two equations
 Example 5.8
User the Kirchhoffs voltage law
To determine the unknown voltage
+ E1 V1 V2 E2 = 0
V1 = E1 V2 E2
= 16 v 4.2v - 9 v
V1 = 2.8v No need to know the
values of the resistors or
the current to determine
the unknown voltage
 Example 5.9
Determine the unknown voltage for the
circuit
E - V1 Vx = 0
Vx = E V1 = 32v -12v = 20v

+ V x V2 V 3 = 0
Vx = V 2 + V 3 both solutions are the same

= 6v + 14 v
Vx = 20 v
 Example 5.10

Determine the voltage V1 & V2

for the network
For path 1: starting at point a in a
clockwise direction
+ 25v - V1 + 15v = 0 V1 = 40v
For path 2:
-V2 - 20v = 0 V2 = -20v

The minus sign indicate that the polarities

are different from those assumed.
Example 5.13
For the series circuit:

a)Determine V2 using Kirchhoffs voltage law

-E + V3 + V2 + v1 = 0 E = V 3 + V2 + v1
V2 = E V1 V3 = 54v - 18v - 15v = 21 v
b)Determine current I2
I2 = V2 / R2 = 21v / 7 = 3A
c)Find R1 & R3
R1 = V1 / I1 = 18v/ 3A = 6
R3 = V3/ I3 = 15v/ 3A = 5
 Find voltages &
loops if

The battery is a 9v battery,

V1= 3.7v, what is the value
of V2
-VB+ V1+ V2= 0
-9v + 3.7v = 5.3 v

V4= 1.3v What is the value

of V3
-V2- V3+ V4= 0
5.3v - V3 + 1.3v = 0
V3 = -5.3 + 1.3 = - 4 v
 Voltage division in a series
circuit
The voltage across series resistive
elements will divide as the
magnitude of the resistance levels
In a series resistive circuit, the
larger the resistance, the more of
the applied voltage it will capture.
The smallest resistor will capture
the least.
The ratio of the voltages across
series resistors will be the same as
the ratio of their resistance level
Voltage divider rule

The majority of
the voltage is
applied to the
1M resistor

Almost the full 100

About 100 mv
About 10 mv
 Voltage divider rule
The voltage divider rule (VDR) permits the
determination of the voltage across a
series resistor without first having to
determine the current of the circuit.
Fist determine the total resistance
Then apply Ohms law to each resistor
Then apply the voltage divider rule
 Voltage divider rule
1st find RT

Applying Ohms law

The resulting format for V1 & V2

Example 5.14

a)How much larger would you expect the

voltage across R2 to be compared to that
across R1?
Since resistor R2 is three times R1, it is
expected that V2 = 3V1
b) Find voltage V1 using only the voltage
divider rule
Example 5.14 cont
C) Using conclusion of part (a), determine
the voltage across R2

d)Use the voltage divider rule to determine

the voltage across R2 & compare your
answer to your conclusion in part (c)

e)How does the sum of V1 & V2 compare to

the applied voltage?
 The voltage divider rule can be extended
to the voltage across two or more series
elements if the resistance in the
numerator is expanded to include the total
resistance of the series resistors across
which the voltage is to be found (R`)
 Example 5.16
Determine the voltage (V`) across the
series combination of resistors R1 & R2
Since the voltage desired is across both
R1 & R2 , the sum of R1 & R2 will be
subtracted as R`
 HW2 pg 161
#21, 25, 27 a &b,