DC Circuits
Basic Concepts
• A Circuit
• Electrical Circuit Variables
• Electrical Circuit Elements or Components
1
What is a circuit?
• An electric circuit is an interconnection of electrical
elements.
• It may consist of only two elements or many more:
2
System of Units
• When taking measurements,
the units are used to quantify
values
• International Systems of Units
(SI)
• Prefixes on SI units allow for
easy relationships between
large and small values
3
Electric Circuit Variables
• Charge
• Current
• Voltage
• Power
4
Charge ( Q
•
•
•
•
•
•
•
)
V
of
is
an
electrical property
the atomic
Which
particle
atom
is
of
①
,
+
made
conserved
from
Matter is made of atoms, each atom consist of
electrons, protons, and neutrons
Charge is a basic SI unit, measured in Coulombs (C).
Counts the number of electrons (or positive charges)
present
Charge on a single electron is 1.602 × 10−19 C
One Coulomb is large unit for charge, 6.24 × 1018
electrons
Realistic or lab value of charge is of the order of pC,
nC, or μC
Charge is always multiple of electron charge
Law of conservation of charge - Charge cannot be
created or destroyed, only transferred
charge
•
or
Charge
is
the
①
atom
5
Current – Flow of Electric Charge
free electrons
•
Electric charge is mobile
•
When a conducting wire (consisting of several atoms) is connected to a battery, the
charges move. Positive charges move in one direction while negative charges move in
opposite direction
•
The movement of charges is called an electric current (electricity)
•
Electricity can be transferred from one place to another, where it can be converted to
another form of energy (electrical to mechanical – motor)
•
The conventional direction of current flow is considered as the direction of
positive charge flow or opposite to the direction of electron (negative charge) flow
-
-
≤ 4
→
conductors
≥ __§n insulators
Annie
→
free
=
electrons
⊖
+
①①
①
to
①
→
e-→ e-
je
→
e-
eI
→
Ccw
→
CW
6
Current
wire,
←a
←a
c- a
← a
←
@
↳ camera
• Electric Current, i, is measured as the charge
moved per unit time through an element
→
𝑑𝑞
𝑖=
𝑑𝑡
↑
• Unit is Ampere (A)
• 1A=
2Trental
=
≈
At
I
=
¥
sea
𝐶𝑜𝑢𝑙𝑜𝑚𝑏
1
𝑠𝑒𝑐𝑜𝑛𝑑
ex
¥•
2 Clsec
=
=
2A
• The charge transferred between time t0 and t will be
𝑡
𝑄 = න 𝑖 𝑑𝑡
𝑡0
7
Current – DC and AC
Constant
current ( not function
of
time
• Direct (DC) Current – remains
constant with time; Battery
• DC current is represented by I
• Alternating Current (AC) –
varies sinusoidally with time;
electricity used at our house to
run an air conditioner,
refrigerator etc.
P
• Symbol used for current varying
w.r.t. time is i
=
Zsinf
:#
3¥;
2A-
3-4/92
¥121T
-2A
'
ta
-
%
8
Direction of Current Flow
• The sign of the current indicates the direction in which the
charge is moving with reference to the direction of interest we
define.
• The conventional direction of current flow is considered as the
direction of positive charge flow or opposite to the direction of
electron (negative charge) flow
• A positive current through a component is the same as a
negative current flowing in the opposite direction.
f⊖
↓
0
①
↓
9
Problem Solving
The current flow through an element is
8𝐴
𝑖=ቐ
8𝑡 2 𝐴
0<𝑡<1
𝑡>1
÷
ga
it
.
Calculate the charge entering the element from t = 0 to t = 2 sec.
A /
f- a)
A / f- 2)
=
=
=
=
0C
Qlt)=
§8dᵗ [
1-
82ft
[26.67 C]
Alt
✓
81-22++0
◦
811-1+811-1 ?
81171-1-(8-1)=26.67
10
Problem Solving
Midtermovnestion
The Current versus time graph is given in Figure 1.a. Sketch the charge versus time graph on
the current versus time graph. Show all the working steps
11
Voltage
• Moving electrons in a conductor in a
particular direction requires energy
• This energy is provided by an
external Electromotive Force (emf) or
Voltage (potential difference), e.g. a
battery
• Voltage vab between two points a and
b in an electric circuit is the energy
required to move a unit charge from b
error
to a
→
𝑣𝑎𝑏
𝑑𝑤
=
𝑑𝑞
=
:?÷=¥
• The potential difference or voltage or
emf is measured in ☐
V → volts
𝐽𝑜𝑢𝑙𝑒
𝐶𝑜𝑢𝑙𝑜𝑚𝑏
1V=1
=1
𝑁𝑚
𝐶𝑜𝑢𝑙𝑜𝑚𝑏
salt
af
tower energy
f)
✓
\
↑
higher energy
( t)
>
bt )
at #
alt )
^
bt)
¥Bt
(
energy
:
)
is
to the charge
carriers to more frm
supplied
a -6
12
Voltage
• vab –> point a is at a potential of vab volts higher than point b or potential at
point a w.r.t b is vab
Alt )
Vab
𝑣𝑎𝑏 = −𝑣𝑏𝑎
161-1
• vab –> vab voltage drop from a to b or vab voltage rise from b to a
• DC Voltage – remains constant with time, represented by V, produced by
a Battery
• AC Voltage – varies sinusoidally with time; represented by v, produced by
an electric Generator
/
alt )
✓ab
Vbn
,
Vab
tbt )
Vab
=
Vba
rise
=
rise
→
of
( vv )
of Gz✓)
Uba
-
=
drop
-7
drop
from 6
from
a
of
C- qv)
from
of
( w)
from
to
a
to
6
a
Uab
6
to
=
a
-
Vba
to 6
13
Power and Energy
• How much power an electric device can handle
• A 100 W lamp gives more light than a 60 W lamp
• Electricity bill charge for the electric energy consumed over
a certain period of time
• Power is the rate of energy provided or consumed per unit
)
scenery
time
•
=i:=n•
𝑑𝑤
𝑝=
𝑑𝑡 → ( time)
• It is measured in Watts (W).
=
p=
UP
• p is the instantaneous power and is the product of voltage
and current
p = vi
14
Passive Sign Convention
• Positive sign for power - power
is being delivered to or absorbed
by the element
• Negative sign for power - power
is being supplied by the element
• A power source, such as a
battery has negative power
"
✓
1-
higher potential ni
( nigher)
Energy
absorbing →
→
element
• Passive sign convention is
satisfied if the direction of current
is selected such that the current
enters through positive terminal
of the voltage and p = +vi and if
the current enters through the
negative voltage terminal p = -vi
-
lower
omen
in
Absorbing Power
+ ✓
PÉffÉ
)
ni Clower
Supplying Power
-
*
→
p=vP
-0¥
i
p=
-
✓
15
Passive Sign Convention and Energy
→En
F-
1-
(4) (3)
=
#
12W
✓
p=tl2W
Absorbing Power
Supplying Power
• Law of conservation of energy – algebraic sum of power in a circuit, at
any instant of time, must be ZERO
• The sum of all power supplied must be absorbed by the other elements
• Energy can be described as watts x time and is measured in Joules (J)
✓ ✗ sec
J
• Power companies usually measure energy in watt-hours
1 Wh = 3600 J
• Energy absorbed or supplied by an element from time t0 to t is:
Sdw=Spdtᵗ =¥
𝑡
𝑡
𝑤 = න 𝑝 𝑑𝑡 = න 𝑣𝑖 𝑑𝑡
𝑡0
𝑡0
vidttvvlto)
wct )
to
16
Problem Solving
Power supplied
P wer absorbed
-
→
→
D=
-
VP
F- VP
Find the power absorbed by each of the elements in the following Figure
4µA
Hov
13=280 W
f-
n
sunlit py=
1-
*
✗
-32W
↑
1nA
17=30×10
yr
=
-3mW
1z✓t↑aYI=Q.tt/o--4A
-
✗
HʳFachexp ;= How
☒
Pz
→
_
how
{ 5=38
,
WtzA=38em✓
17
Plt :o)
Problem Solving
-_
8+120=16 on
plt=2Dl2✗a=ow
The voltage and current at the
terminals of a circuit element are
shown in figure below. Sketch
the power versus time graph for
0<t<20 ksec
•
HA
9×14=126
P / f- 5)
Plt -155-11×8=884
=
w
F- VP
2%+71-+8
✓
✓
( f-
It -5sec
)=¥✗ñ(
⑤ +8
=T✓
15sec
)=¥( b) +8
=u✓
put
v.int#*hM..wi=-mt-3P---lm4t2A
18
Circuit Elements or Components
• Element is a basic building block of an electric circuit
• Electric circuit is an interconnection of the elements
• Circuit analysis – determining the voltages across and current through
the circuit elements
Two types:
• Active
• Passive
Active elements can generate energy
•
Generators
•
Batteries
•
Operational Amplifiers
Passive elements absorb energy
•
Resistors
•
Capacitors
•
Inductors
19
?⃝
Activeelements-T-de.nl
Independent
i
/
Tv
±
Voltage
source
¥
,
i¥ÉEH
§
="
111.
:: :::::
2A
✓i
volts
Voltage ±
Current
ZV
/
ZV
^
source
Source
Vc
µ
cars
zi
A
Vc
cc
=
=
Voltage
control
current
central
A
°
sv¥FFni
fi
indrp
✓ s
CCVS
( voltage
sour
Passive
(A)
elements
Resistance -7
:
Resistor
ability
to resist
Active Element - Ideal Independent
Voltage Source
• An ideal voltage source provides a specified voltage that is
independent of the other circuit elements
• An ideal voltage source has no internal resistance
• Voltage at its terminals remains constant independent of the
current drawn from the source
• Car battery, flash light battery
20
Active Element - Ideal Independent
Current Source
• Current sources are the opposite of the voltage source
• They have infinite internal resistance
• They will generate any voltage to establish the desired
current through them
• Current at its terminals remains constant independent of
the voltage
21
Active Element - Dependent (Controlled)
Sources
A dependent source has its
output controlled by another
voltage or current variable
Symbolically represented as a
diamond.
Four types:
• A voltage-controlled voltage source
(VCVS)
• A current-controlled voltage source
(CCVS)
• A voltage-controlled current source
(VCCS)
• A current-controlled current source
(CCCS)
22
Dependent Source example
Current controlled voltage source
23
Problem Solving
F- VI=V=¥
For the following circuit, complete the table below
is
current
in
same
series
"
^
¥%→
•
=
"
6A
'
%
I "
P ] -8A
NSA
•
'
-
l¥¥→
Io
-6A
-
-ᵗ¥s¥÷
.
Component
Number
1
2
3
4
5
6
7
8
Voltage
20
Current
3
8
Power
60
Power (Absorbed or
Supplied)
If
-_
1A
A
3
5
16
20
12
5
6
2
924
Problem Solving
For the following circuit, complete the table below
+ bA
③
+
t
-
±
-
}
"
✓
172
2×9=72 ✓
÷¥¥ Y¥÷
=
.
^↳
vi. -4N
¥÷%%→=
w=68✓
Component
Number
1
2
3
4
5
6
7
8
Voltage
20
-7%
68
16
20
12
8V
Current
3
Power
60
3
z
S
5
6
2
I
120
576
340
Power (Absorbed or
Supplied)
Wq=f✓
.
qg=664W✓
EA
-664mV
-
5
5
A
5
80
A
120
24
S
s
8
A
25
Passive Element - Resistor
Resistance (R) – is a property of a material to resist
the flow of electric current
Resistance of an object is a function of its length, l,
cross sectional area A and the material’s resistivity
l
R=
A
The resistance is measured in Ohms (Ω)
Resistivity is in ohm-m
Good conductors, copper and aluminum, has low
resistivities
Insulators, mica and paper, has high resistivities
26
Passive Element - Resistor
Resistivity
27
Passive Element - Resistor
Circuit element used to model the current resisting
behaviour of a material is a RESISTOR.
28
Resistance - Resistor
The resistance of a resistor determines how much current it will carry
when a given voltage is applied across it
A resistor’s nominal value and its tolerance is described by color
codes on the resistors
The tolerance means that the actual value of the resistor is
guaranteed to be within this amount of its nominal value
29
Resistance - Resistor
30