ELE1110A Tutorial1 Circuit Elements

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ELE1110A Tutorial-1Circuit Elements Law

• A.J.

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Outline

• Reference Direction
• Power Energy
• Resistor Ohms Law
• Voltage Current Sources
• Network Topology
• KCL KVL
• Series Parallel Resistors
• Y-? Transformation

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Reference Direction

• Since the actual direction of current or voltage
  may be unknown or variable, it is necessary to
  assume the reference directions for them.
• The reference direction for voltage is indicated
  by the and - signs near the terminals.
• The reference direction for current is indicated
  by the arrow.
• Given the reference direction, if the calculated
  i / v turns to be positive, it means the actual
  direction of i / v is consistent with the
  reference direction conversely, negative sign
  means the reverse.
• Associated reference direction For a circuit
  element, we usually use a convention that the
  reference directions of the current through it
  and the voltage drop across it are consistent, as
  shown in the left figure.

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Power Energy
Standard Unitsi A (ampere), q C (coulomb),
v volt (V), p W (watt), w J (joule) Given
condition that the reference directions of v
across the element and i through the element are
associated, pgt0, the element absorbs powerplt0,
the element releases power. Active elements
can generate energy (voltage and current
sources)Passive elements cannot generate
energy (resistors, capacitors and inductors)
notice that capacitors and inductors can store
energy
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Resistor Ohms Law

• The linear resistor is an ideal circuit element
  that obeys Ohms Law.
• Ohms Law Given condition that the reference
  directions of v across the resistor and i through
  the resistor are associated, the following
  relation holds
• where R is a positive real constant, called
  resistor.
• The conductance G is defined as the reciprocal of
  R
• Standard Units R W (ohm), G S (Siemens)
• Power Energy for linear resistor
• Since R and G are positive real constants, pgt0.
  Thus linear resistor always consumes electric
  power which is transformed into heat.

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Voltage Current Sources

• Independent source Its magnitude may be DC or
  AC, but does not depend on other voltages or
  currents in the circuit.
• Dependent source Its magnitude is a function
  of another voltage or current in the circuit.
• Voltage Controlled Voltage Source VCVS, m 1
• Current Controlled Voltage Source CCVS, R W
• Voltage Controlled Current Source VCCS, G S
• Current Controlled Current Source CCCS, b 1

Independent current source
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Network Topology

• A Network is an interconnected set of electrical
  components.
• A Branch represents a single element
• Note that a series connection can be considered
  as one branch.
• A Node is the point of connection between two or
  more branches.
• Note that group of nodes connected only by wires
  should be considered as one big node in circuit
  analysis.

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Network Topology

• A Loop is any closed path in a circuit
• Mesh, Tree, Tree branch, Connection branch,
  Independent loop
• A relationship is valid for a closed circuit
• where b is the branches, n the nodes, l the
  independent loops.
• Series Connection two or more elements are
  connected sequentially and consequently carry the
  same current.
• Parallel Connection two or more elements are
  connected to the same two nodes and consequently
  have the same voltage across them.

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KCL KVL

• KCL
• The algebraic sum of all the currents at any node
  in a circuit equals zero.
• Alternative form
• Sum of currents flowing into a node Sum of
  current flowing out of the node
• KVL
• The algebraic sum of all the voltages around any
  loop in a circuit equals zero.
• Alternative form
• Sum of voltage drops Sum of voltage rises
• (We can introduce a rotation direction to help
  determine the voltage signs)

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Series Parallel Resistors

• Series Resistors and Voltage Division
• Parallel Resistors and Current Division
• When k 2,

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Y-? Transformation
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Example 1
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Example 2
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Example 3How to solve the following circuit?
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Example 4
Find V0/Vs in terms of a I0 Vs/(R1R2) V0
-a I0 ( R3R4/ (R3R4) ) So V0 / Vs -a R3R4
/ (R1R2)(R3R4)