Basic Laws

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Basic Laws

• Instructor Chia-Ming Tsai
• Dept. of Electronics Engineering
• National Chiao Tung University

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Contents

• Ohms Law (resistors)
• Nodes, Branches, and Loops
• Kirchhoffs Laws
• Series Resistors and Voltage Division
• Parallel Resistors and Current Division
• Wye-Delta Transformations

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Ohms Law

• Resistance R is represented by
• Ohms Law

1 ? 1 V/A
ohm
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Resistors
Open circuit
Short circuit
Variable resistor
Potentiometer (pot)
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Nonlinear Resistors
Linear resistor
Nonlinear resistor
v

• Examples lightbulb, diodes
• All resistors exhibit nonlinear behavior.

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Conductance and Power Dissipation

• Conductance G is represented by

positive R power absorption () negative R
power generation (-)
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Nodes, Branches, Loops

• Branch a single element (R, C, L, v, i)
• Node a point of connection between branches (a,
  b, c)
• Loop a closed path in a circuit (abca, bcb, etc)
• An independent loop contains at least one branch
  which is not included in other indep. loops.
• Independent loops result in independent sets of
  equations.

redrawn
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Continued
Elements in series
Elements in parallel

• Elements in series
• (10V, 5?)
• Elements in parallel
• (2?, 3?, 2A)
• Neither
• ((5?/10V), (2?/3?/2A))

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Kirchhoffs Laws

• Introduced in 1847 by German physicist G. R.
  Kirchhoff (1824-1887).
• Based on conversation of charge and energy.
• Two laws are included, Kirchhoffs current law
  (KCL) and Kirchhoffs votage law (KVL).
• Combined with Ohms law, we have a powerful set
  of tools for analyzing resistive circuits.

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KCL

• Assumptions
• The law of conservation of charge
• The algebraic sum of charges within a system
  cannot change.
• Statement
• The algebraic sum of currents entering a node (or
  a closed boundary) is zero.

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Proof of KCL
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Example 1
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Example 2
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Case with A Closed Boundary
Treat the surface as a node
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KVL

• Assumption
• The principle of conservation of energy
• Statement
• The algebraic sum of all voltages around a closed
  path (or loop) is zero.

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Proof of KVL
i
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Example 1
Sum of voltage drops Sum of voltage rises
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Example 2
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Example 3
Q Find v1 and v2.
Sol
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Example 4
Q Find currents and voltages.
Sol
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Series Resistors
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Voltage Division
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Continued
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Parallel Resistors
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Current Division
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Continued
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Brief Summary
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Example
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How to solve the bridge network?

• Resistors are neither in series nor in parallel.
• Can be simplified by using 3-terminal equivalent
  networks.

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Wye (Y)-Delta (?) Transformations
Y
T
?
?
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? to Y Conversion
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Y-? Transformations
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Example