Download ECE 2006 - Lecture 2

ECE 2006
Lecture for Chapters 1 & 2
S.Norr
Fundamental Laws of Circuits
• Ohm’s Law:
– The voltage across a resistor is directly
proportional to the current through it.
– The constant of proportionality is called
Resistance
Resistance
• The electrical resistance, R, of a material
is dependent on its Resistivity, Length and
Cross-Section.
• Examples: Copper has a Resistivity of 1.7
x 10-8 Ohm-meters. Glass has a
Resistivity of about 1012 Ohm-meters.
Conductance
• Conductance, G, is the inverse of
Resistance
• It is sometimes easier to consider the
Conductance of a material instead of its
Resistance.
G=1/R=I/V
Open/Short Circuits
• A circuit element having no resistance is
considered to be a Short Circuit (infinite
conductance)
• A circuit element having infinite resistance
is considered an Open Circuit (zero
conductance)
Circuit Topology
• Branch – Part of a circuit containing only one
element, such as a resistor or a source.
• Node – A point of connection between two or
more Branches
• Loop – Any closed path contained within the
circuit of interest
Series and Parallel
• Two (or more) branches are in Series if
they share a single node exclusively.
– Branches in Series carry identical current
• Two (or more) branches are in Parallel if
they connect to the same two nodes
– Branches in Parallel have identical voltage
Types of Branches
• Branches that are a Source of Energy:
• Branches that are a Load (Dissipate
Energy):
Resistor
Counting Branches and Nodes
• The number of Branches in a circuit is the
same as the number of circuit elements
• The number of nodes is representative of
all places in the circuit where branches
connect
Kirchhoff’s Laws
• Based of the Law of Conservation of Charge
(conservation of energy): The algebraic sum of
charges within a closed system cannot change.
• KCL – Kirchhoff’s Current Law: The algebraic
sum of currents entering a node (or any closed
boundary) is Zero.
• KVL – Kirchhoff’s Voltage Law: The algebraic
sum of voltages around a Loop (or any closed
path) is Zero/
KCL
• Application of KCL is straightforward
KVL
• Use care in assessing each voltage as a
drop or rise:
Series Resistors
• Elements in series each see the same current
• Resistors in series add
directly:
• Rac = Rab + Rbc
• Conductances in series add as the inverse of the
sum of their inverses
Voltage Division
VR = Vs*Same/Sum
Resistors in Parallel
• Elements in parallel are each impressed
with the same voltage
• Resistors in parallel add as the inverse of
the sum of their inverses
• Conductances in parallel add directly
Current Division
• IR = IS*Opp/Sum
Delta-Wye Transform
• Resistors in a delta shaped arrangement
can be transformed into the corresponding
wye shaped circuit:
Rx = Adj*Adj/Sum
Wye-Delta Transform
• Resistors in a wye shaped arrangement
can be transformed into the corresponding
delta shaped circuit:
Rx = Sum of Product Terms/Opposite