8. Units and Dimensions
The System International (SI) Unit
8
Unit abbreviation
Unit
Quantity
Kg
Kilogram
Mass
m
meter
Length
s
second
Time
A
Ampere
Electrical Current
K
Kelvin
Thermodynamic Temperature
cd
candela
Luminous Intensity
mol
mole
Amount of Substance
rad
radian
Plane Angle
sr
steradian
Solid Angle
9. Units and Dimensions Contd.
The System International (SI) Unit
9
Value
Abbreviation
Submultiple
Value
Abbreviation
Multiple
10-3
m
milli
1018
E
exa
10-6
µ
micro
1015
P
peta
10-9
n
nano
1012
T
tera
10-12
p
pico
109
G
giga
10-15
f
femto
106
M
mega
10-18
a
atto
103
K
kilo
10. Circuit Elements
➢A voltage or current source of energy (Active elements);
➢Resistors, Inductors and Capacitors (Passive elements).
Energy Sources
• Two basic variables in electric circuits: electric current & electric
potential difference (Voltage).
• A source of energy is required to cause a current to flow and
thereby to produce electric voltages in various parts of the
circuit.
• Energy is work and is measured in joules (J).
When a force F (newton) moves a body through a distance d
(metres) the work done is (F x d ) joules.
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11. Circuit Elements Contd.
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Voltage Source
An ideal voltage source is independent of the current through it.
Its electromotive force (emf) or voltage is a function of time only.
The unit is called the volt (V).
12. Circuit Elements Contd.
• If a thick copper wire were connected across its ends the
current through it would be infinite.
Therefore,
The electric potential difference between two points is the work
required to move a unit positive charge (i.e. 1 C) between them.
12
14. Circuit Elements Contd.
14
Current Source
An ideal current source is independent of the voltage across it.
When 1 C of charge passes a given plane of reference in one
second, it represents a current of 1 A
I = dQ /dt (2.1)
When a current of (I ) amperes flows for (T ) seconds, the
charge moved is given by
𝑄 =
0
𝑇
𝐼 𝑑𝑡 (2.2)
16. Circuit Elements Contd.
Resistance
Materials within which charges can move easily are called
conductors. e.g. Copper, Aluminum, etc.
The resistance of a conductor is directly proportional to its length
(L) and inversely proportional to its cross-sectional area (A).
➢R α L ;
➢R α 1/ A ;
➢R α ρ ;
➢R α L / A ;
➢R = ρ L / A (Ω)
where ρ is the constant of proportionality and is called the
resistivity of the material of the conductor. 16
17. Circuit Elements Contd.
Ohm’s Law
• Ohm’s law states that the voltage v across a resistor is directly
proportional to the current I flowing through the resistor.
• V α I
• Ohm defined the constant of proportionality for a resistor
to be the resistance R.
• V = R I
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20. Circuit Analysis
Definition of Terms
Node: a point at which two or more elements have a common
connection is called a node. There are six nodes in the circuit,
numbered 1- 6.
Open circuit: if the resistor R1 was removed from the circuit
then, there is said to be an open circuit between nodes 1 and 2.
Branch: a single element or group of elements with two
terminals which form the only connections to other single
elements or groups of elements.
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21. Circuit Analysis Contd.
Branch current: the current flowing in a branch is called a
branch current. Currents I1, I2 and I3 in the diagrams are
branch currents.
Mesh: a path through two or more branches which forms a
closed path.
Mesh current: the currents Ia and Ib are called mesh currents.
Short circuit: the connection between nodes 4, 5 and 6 is
made with a piece of wire having virtually no resistance and is
called a short circuit.
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22. Circuit Analysis Contd.
Kirchhoff's Current Law (KCL)
The sum of the currents entering a node is equal to the sum of
the currents leaving that node.
I 1 + I 2 + I 3 = I 4+ I 5
The algebraic sum of the currents meeting at a node is equal to
zero.
I 1 + I 2 + I 3 −I 4 − I 5 = 0
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23. Circuit Analysis Contd.
Kirchhoff's Voltage Law (KVL)
The sum of the voltage sources around any closed path is
equal to the sum of the potential drops around that path.
The algebraic sum of all the potential differences around any
closed path is equal to zero.
− I 3 R3 + V − I 1 R1 = 0
V = I 1 R1 + I 3 R3
I 2 R2 + 𝐼1 R1 −V= 0
V = I 1 R1 + I 2 R2
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