1. Circuit Elements and Variables
Chapter 1
Circuit Elements and Variables

2. What is Electric Circuit?
An electric circuit is an interconnection of electrical elements
Example: Consists of 3 basic elements: battery, lamp, connecting wires.
When the wires are connected properly, the circuit is said to be closed and the lamp will light. When the wires are disconnected, the circuit is said to be open.

3. Circuit Diagram

4. Basic Electric Concept
Review SI unit (International Systems of Unit)
Know the definition of basic electrical quantities : charge, current, voltage, power & energy
Know the symbols and definition of the elements of the circuit:
passive and active elements & independent and dependent sources
To understand some fundamentals laws and basic network to determine the values of electric circuit variables:
Ohm’s Law, nodes, branches, loops & Kirchoff’s Law

5. Review SI Units (1)
SI: International System of Unit is used by all the major engineering societies and most engineers throughout the world.

6. Review SI Units(2)
Standardized prefixes to signify powers of 10

7. Basic Electric Concept
Review SI unit (International Systems of Unit)
Know the definition of basic electrical quantities :
charge, current, voltage, power & energy
Know the symbols and definition of the elements of the circuit:
passive and active elements & independent and dependent sources
To understand some fundamentals laws and basic network to determine the values of electric circuit variables:
Ohm’s Law, nodes, branches, loops & Kirchoff’s Law

8. Unit, Symbol and Definition
Quantity
Unit
Symbol
Charge, Q
Coulomb C
Current, I
Ampere A
Voltage, V
Volt V
Power, P
Watt W
Energy, W
Joule J
Quantity
Definition
Charge, Q
Electric charge is a property of the atomic particles possessed by both electrons and protons.
Current, I
Current is the movement of charge in a specified direction.
Voltage, V
Voltage (or potential difference) is the energy required to move a unit charge through an element
Power, P
Power is the time rate of expending or absorbing energy.
Energy, W
Energy is the capacity to do work

9. Charge, Q (C)
The charge on one electron is called electronic charge and equivalent to Q of e =  C How many electrons in 1 C? 1 C = 1 /  = 6.24 x 1018 electrons

10. Alternating current (AC)
Current, I (A)
Current is the movement of charge in a specified direction.
Charge dQ
C/s
Current =
I (A) = dt
Time
2 common types of current:
Direct current (DC)
Alternating current (AC)

11. Voltage, V (v) Energy dW Voltage = vab = dQ Charge
Voltage (or potential difference) is the energy required to move a unit charge through an element
It is a potential energy difference between two points, a and b
Energy dW
Voltage =
vab = dQ
Charge

12. absorbing power supplying power
Power, P (W)
Power is the time rate of expending or absorbing energy.
Energy dW
Power =
P = dt
Time i + – v i + – v
P = +vi P = –vi
absorbing power supplying power

13. Energy, W (J)
Energy is the capacity to do work, measured in joules (J).

14. Basic Electric Concept
Review SI unit (International Systems of Unit)
Know the definition of basic electrical quantities : charge, current, voltage, power & energy
Know the symbols and definition of the elements of the circuit:
passive and active elements & independent and dependent sources
To understand some fundamentals laws and basic network to determine the values of electric circuit variables:
Ohm’s Law, nodes, branches, loops & Kirchoff’s Law

15. Active and Passive Elements
Circuit Elements
Active elements
capable of generating electric energy
Example : generators, batteries, operational amplifier, voltage and current sources
Passive elements
incapable of generating electric energy
Example : resistor, inductor, capacitor

16. Independent Source AC DC
Voltage
(+/- sign)
Current
(arrow)

17. Dependent Source
A dependent source is an active element in which the source quantity is controlled by another voltage or current.
They have four different types:
VCVS: Voltage-controlled voltage source
CCVS: Current-controlled voltage source
VCCS: Voltage-controlled current source
CCCS: Current-controlled current source

18. Dependent Source (Diamond shape)
Current
(arrow)
Voltage
(+/- sign)

19. Example of sources Current controlled voltage source, V =10 i
Independent voltage source
V =20 V
Current controlled current source,
Is =10.2 I

20. Basic Electric Concept
Review SI unit (International Systems of Unit)
Know the definition of basic electrical quantities :
charge, current, voltage, power & energy
Know the symbols and definition of the elements of the circuit:
passive and active elements & independent and dependent sources
To understand some fundamentals laws and basic network to determine the values of electric circuit variables:
Ohm’s Law, nodes, branches, loops & Kirchoff’s Law

21. Ohms Law
Ohm’s law states that the voltage across a resistor is directly proportional to the current I flowing through the resistor.
Two extreme possible values of R:
R = 0 : short circuit
R =  : open circuit.

22. Short Circuit
R = 0 , no voltage difference exists, thus V = 0 V, but current still can flow.

23. Open circuit
R =  , no current flows .Voltage difference can exist, as determined by the circuit

24. Conductance & Power
Conductance is a measure of the ability of an element to conduct electric current
Inverse of resistance
The units is Siemens (S) or mhos
Power dissipated by resistor:

25. Example 1
In the circuit, calculate the current I, the conductance G, and the power P.

26. Example 2
In the circuit, calculate the voltage V, the conductance G, and the power P.

27. Branches
A branch represents a single element such as a voltage source or a resistor.
In other words, a branch represents any elements which has two terminals. 4 1 2 3

28. Exercise
Should we consider it as one branch or two branches?

29. Nodes A node is the point of connection between two or more branches.
A node usually indicated by a dot in a circuit.
If a short circuit (no element between dots), the multiple dots constitute as a single nodes.
How many branches connected to node a, b and c?

32. Loops
A loop is any closed path in a circuit.

33. Relation of branches, nodes and loops
A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology:

34. Example 3 How many branches, nodes and loops are there?
Does it satisfy b = l + n -1?

35. Kirchhoff Law Gustav Robert Kirchhoff (1824–1887)
Models relationship between:
circuit element currents (KCL)
circuit element voltages (KVL)
Introduce two laws:
Kirchhoff Current Law (KCL)
Kirchhoff Voltage Law (KVL)

36. Kirchhoff’s Current Laws (KCL)
Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.

37. Kirchhoff’s Current Laws (KCL)
Convention sign for current entering and leaving node:
current entering node = + i
current leaving node = - i
According to KCL, for any node:
Without the sign (+Ve or -Ve), the formula of KCL can be written as:
Current entering node = current leaving node
(What goes in, must comes out)
N = number of branches connected to the nodes
in = nth current entering (+ i) or leaving (- i) the node

38. Example of KCL (1) Node A 2 options:
Current entering = current leaving
Node A
Current leaving node, (-i)
Current entering node, (+i)

39. Example of KCL (2) Node a IT : Leaving node a (-Ve)
I1 : Entering node a (+Ve)
I2: Leaving node a (-Ve)
I3: Entering node a (+Ve)

40. Kirchhoff’s Voltage Laws (KVL)
Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero.

41. Kirchhoff’s Voltage Law (KVL)
For any circuit loop:
Convention sign for voltage inside loop (clockwise or anticlockwise direction):
If the positive terminal of voltage is met first: +V
If the negative terminal of voltage is met first: -V
Without the +/- sign, KVL formula can be written as
Sum of voltage drops = sum of voltage rises
M = number of voltages in the loop
vm = mth voltage

42. Example of KVL +V +V -V -V +V Voltage drop Voltage drop Voltage rise

44. Example 4
Find v1 and v2 using KVL and Ohm’s Law.

45. Example 5
Find v1, v2 and v3 using Ohm’s Law KCL and KVL.

46. Example 6
Determine vo and I in the circuit