ECE 1311: Electric Circuits
Chapter 2: Basic laws
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
l
A
•
•
•
•
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
Ohm’s Law (1)
 Ohm’s law states that the voltage across a resistor is directly
proportional to the current flowing through the resistor.
v

iR
 Only material with linear relationship satisfy Ohm’s law
(note the PSC)
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.
1 i
G 
R v
 The power dissipated by a resistor:
2
v
p  vi  i 2 R 
R
 Power absorbed by R is always positive
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:
b  l  n 1
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
v  iR
I
V
n
0
n
0
 These law alone are sufficient to analyze many circuits
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)
Delta -> Y
Y -> Delta
Rb Rc
R1 
( Ra  Rb  Rc )
Ra 
R1 R2  R2 R3  R3 R1
R1
Rc Ra
R2 
( Ra  Rb  Rc )
Rb 
R1 R2  R2 R3  R3 R1
R2
Ra Rb
R3 
( Ra  Rb  Rc )
Rc 
R1 R2  R2 R3  R3 R1
R3
Wye-Delta Transformation (2)
Practice 2.10
Practice 2.11
Practice 2.12