CSCI 2980: Introduction to Circuits, CAD, and Instrumentation
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Transcript CSCI 2980: Introduction to Circuits, CAD, and Instrumentation
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(t2 ) 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 ), R 0
1 Ω = 1 V/A (Ω: ohm, V: volt, A: ampere)
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 ),
v 2 (t )
Ri (t )
R
R0
2
Conductance G (unit: siemens S)
p(t ) v(t )i (t )
G
1S=1A/V
1
R
i (t ) Gv(t )
i 2 (t )
p(t )
Gv2 (t )
G
Two specific values of resistance
+
v0
Short Circuit
R0
i0
v(t ) Ri(t ) 0
Open Circuit
R
v (t )
i (t )
0
R
Example 2.1: Determine voltage, current, and power absorbed by resistor