EENG 2610: Circuit Analysis
Class 1: Basic Concepts, Ohm’s Law
Oluwayomi Adamo
Department of Electrical Engineering
College of Engineering, University of North Texas
Electro-technology is driving force in all engineering discipline
Circuit analysis is fundamental to electro-technology
Power Grid
Motherboard of Computer
Integrated Circuits (IC chips)
Basic Strategy in Circuit Analysis
Typical Electric Circuit
ELECTRIC CIRCUIT IS AN INTERCONNECTION OF ELECTRICAL COMPONENTS
2 TERMINALS COMPONENT
a
b
NODE
characterized by the
current through it and
the voltage difference
between terminals
NODE
The concept of node is extremely important.
We must learn to identify a node in any shape or form
BASIC CONCEPTS
LEARNING GOALS
•System of Units: The SI standard system; prefixes
•Basic Quantities: Charge, current, voltage, power and energy
•Circuit Elements: Active and Passive
International System of Units – SI Standard System
Standard SI Prefixes
SI prefixes used to form decimal multiples and submultiples of SI units.
These standard prefixes are employed throughout our study of electric circuits.
Basic Quantities

Electric Charge (unit: coulomb)



The most elementary quantity in electric circuit analysis
Charged particle in matter: electron (-), proton (+), neutron (no charge)
Electric Circuit



Q, q, q(t)
A pipeline where electric charge can be transferred from one point to
another
An interconnection of electrical components, each of which we will
describe with a mathematical model
Electric Current (unit: ampere)
i, i(t)

The time rate of change of charge:


1 A = 1 C/s (A: ampere, C: coulomb, s: second)
Conventional current flow represents the movement of positive charges,
even though in metallic conductors current flow is resulted from the motion
of electrons, negative charge.
I = 2 A means 2 C of charge pass from left to right each second

Must specify both magnitude and direction:

Basic Quantities

Two types of current we will study in this course



i (t )
i (t )
AC
Alternating current (AC)
Direct Current (DC)
t
Voltage (or potential) between two points in a circuit (unit: volt)

Defined as the difference in energy level of
a unit charge located at each of the two points:

The energy required to move a unit positive charge is the defined voltage
1 V = 1 J/C = 1 N·m/C (V: volt, J: joule, C: coulomb, N: newton, m: meter)




v
dw
dq
The + and – signs define a reference direction for V
A unit charge moved between A and B will have energy change
Must specify both magnitude and direction
DC
t
Basic Quantities

Energy and Energy Transfer
W, w(t)
Vbattery
Vbulb
Charges gain
energy as passing



Charges spend
Energy as passing
When the element is absorbing energy, a positive current enters the
positive terminal and leaves via the negative terminal.
When the element is supplying energy, a positive current enters the
negative terminal and leaves via the positive terminal.
A negative current in one direction is equivalent to a positive current in the
opposite direction, and vice versa. The same is the voltage.
Basic Quantities

Power (unit: watt)
P, p(t)

Defined as the time rate of change of energy:

The change in energy in a period of time:
p(t ) 
dw(t ) dw(t ) dq(t )


 v(t )i (t )
dt
dq(t ) dt
t2
t2
t1
t1
w  w(t 2 )  w(t1 )   p(t ) dt   v(t )i (t ) dt


1 W = 1J/s = 1 V·A (W: watt, J: joules, V: volt, A: ampere)
Passive Sign Convention – Sign Convention for Power


Variables for the current and voltage should be arranged as shown in the figure:
Current enters an element via positive voltage reference point
i (t )
+
v (t )
Power:

p  v(t )i (t )
-
Circuit
Element
If the sign of power is positive, power is being absorbed by the element; if the sign
is negative, power is being supplied by the element.
Example 1.2: Determine whether the elements are supplying or receiving power and how much
Circuit Elements


In general, all elements will be terminal devices that are completely
characterized by the current through the element and the voltage across it.
Active or passive elements



Passive Elements



Maintain a specified voltage
between its terminals regardless
of the current through it.
Independent Current Source


Resistor, Capacitor, Inductor
We will define these in coming classes
Independent Voltage Source


Active element is capable of generating energy.
Passive element cannot generate energy.
Maintain a specified current
between its terminals regardless
of the voltage across its terminals.
Independent sources normally
supply energy, but they can
also absorb energy
Circuit Elements

Dependent (or Controlled) Sources


Unlike independent sources, dependent (or controlled) sources
generate a voltage or current that is determined by a voltage or
current at a specified location in the circuit.
Four different types of dependent sources:
Voltage
Controlled
Sources
Current
controlled
Sources
The Principle of Conservation of Energy

Power supplied in a circuit network is exactly equal to the power
absorbed. Electrical circuits satisfy this principle
Example 1.7: Use power balance to compute I0
Ohm’s Law

Ohm’s Law




Defines a passive element Resistor R (unit: ohm)
It only absorbs power; converts electrical energy
to thermal energy
Ohm’s Law: The voltage across a resistor is directly
proportional to the current flowing through it:
v(t )  R  i (t ),
1 Ω = 1 V/A (Ω: ohm, V: volt, A: ampere)
R0
v (t )
Linear
approximation
Linear range
Actual v-I relationship
i (t )
Ohm’s Law

Power absorbed by a resistor
v(t )  R  i (t ),

2
v
(t )
 Ri 2 (t ) 
R
R0
Conductance G (unit: siemens S)


p(t )  v(t )i(t )
1S=1A/V
1
G
R
i(t )  Gv(t )
i 2 (t )
p(t ) 
 Gv2 (t )
G
Two specific values of resistance
+
v0

Short Circuit
R0
i0
v(t )  Ri (t )  0
Open Circuit
R
i (t ) 
v(t )
0
R
Example 2.1: Determine voltage, current, and power absorbed by resistor