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Chapter 2: Basic laws
ECE 1311: Electric Circuits
Basic Law Overview
Ideal sources – series and parallel
Ohm’s law
Definitions – open circuits, short circuits, conductance,
nodes, branches, loops
Kirchhoff's law
Voltage divider and series resistors
Current divider and parallel resistors
Wye-Delta transformations
Ideal Voltage Source
Ideal voltage source in series can be added
Ideal voltage source in parallel = NO GOOD
Recall: ideal voltage source guarantee the voltage between
two terminals is at the specified potential (voltage)
BOOM
Ideal Current Source
Ideal current source cannot be connected in series
Ideal current source in parallel can be added
Recall: ideal current guarantee the current flowing through
source is at the specified value
Recall: Current entering a circuit must be equal to the
current leaving the circuit
BOOM
Resistance
All material resist the flow of current given by R • R = resistance of an element in ohms
• p = resistivity of material in ohm-meters
• l = length of material in meters
• A = cross sectional area of material in meter2
A
lR
Ohm’s Law (1)
Ohm’s law states that the voltage across a resistor is directly
proportional to the current flowing through the resistor.
Only material with linear relationship satisfy Ohm’s law
(note the PSC)
iRv
Ohm’s Law (2) Two extreme possible values of R: 0 (zero) and (infinite) are
related with two basic circuit concepts: short circuit and open
circuit.
Conductance is the ability of an element to conduct electric current; it is the reciprocal of resistance R and is measured in mhos or siemens.
The power dissipated by a resistor:
Power absorbed by R is always positive
v
i
RG
1
R
vRivip
22
Practice 2.1
Short circuit
An element (or wire) with R = 0 is called a short circuit
An ideal voltage source with V = 0 is equivalent to a short
circuit
Since v = iR and R = 0, v = 0 regardless of i
Recall: cannot connect voltage source to a short circuit
Open circuit
An element with R = is called the open circuit
Often represented by a wire with an open connection
An ideal current source I = 0A is also equivalent to an open
circuit
Recall: cannot connect current source to an open circuit
Formalization
For this course, networks and circuits will be used
interchangeably
Networks are composed of nodes, branches and loops
Nodes, Branches and Loops
A branch represents a single element such as a voltage
source or a resistor.
A node is the point of connection between two or more
branches.
A loop is any closed path in a circuit.
A network with b branches, n nodes, and l independent
loops will satisfy the fundamental theorem of network
topology:
1 nlb
Practice 2.2
How many branches, nodes and independent loops are there?
Practice 2.3
How many branches, nodes and loops are there?
Overview on Kirchhoff’s Law
It’s the foundation of circuit analysis
There are two - Kirchhoff’s current law (KCL) and
Kirchhoff’s voltage law (KVL)
It tell us how the voltage and current are related within a
circuit element are related
Kirchhoff’s Current Law (1)
Kirchhoff’s current law (KCL) states that the algebraic
sum of currents entering a node (or a closed
boundary) is zero.
i.e. the sum entering a node is equal to the sum leaving a
node – based on the law on conservation charge
Kirchhoff’s Current Law (2)
KCL also apply at the boundary
Practice 2.4
Given that essential node is the point between 3 or more
branches,
Kirchhoff’s Voltage Law (1)
Kirchhoff’s voltage law (KVL) states that the algebraic
sum of all voltages around a closed path (or loop) is zero.
Based on the conservation of energy
Practice 2.5
Practice 2.6
Apply KVL to find the value I
Summary on Ohm’s Law, KCL and KVL
Ohm’s Law
KCL
KVL
These law alone are sufficient to analyze many circuits
0
0
n
n
V
I
iRv
Practice 2.7
Find v2, v6 and vI
Practice 2.8
Find i0 and v0
Practice 2.9
Resistor Circuit Overview
Resistors in series
Resistors in parallel
Voltage dividers
Current dividers
Wye-Delta transformation
Resistors in series
Resistors in Parallel (1)
Resistors in Parallel (2)
Voltage Divider
Current Divider
Resistor Network
Knowing equivalent and parallel equivalents of resistors is
not enough
Wye-Delta Transformation (1)
)(1
cba
cb
RRR
RRR
)(2
cba
ac
RRR
RRR
)(3
cba
ba
RRR
RRR
1
133221
R
RRRRRRRa
2
133221
R
RRRRRRRb
3
133221
R
RRRRRRRc
Delta -> Y Y -> Delta
Wye-Delta Transformation (2)
Practice 2.10
Practice 2.11
Practice 2.12