Basic circuit theory

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Basic circuit theory
Sensors Technology MED4

Lecturer Smilen Dimitrov
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Introduction

• The model that we introduced for ST

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Introduction

• We have discussed
• The units of voltage, current and resistance, in
  terms of electric circuits
• The definition of an elementary electric circuit
• Ohms law

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Resistors

• Construction of resistors
• Different sizes for different power ratings
• As far as construction of resistors goes,
  generally we can discern
• Carbon Composition Resistors
• Film Resistors
• Carbon Film Resistors
• Metal Film Resistors
• Metal Oxide Resistors
• Wire Wound Resistors

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Resistors color code

• Ratings of resistors written as color code

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Basic circuit theory

• Electrical circuit is a mathematical model that
  approximates the behavior of an actual electrical
  system. Circuit theory consists of models and
  mathematical techniques
• Circuits (also known as 'networks') are
  collections of circuit elements and wires.
• Electric circuits will be considered as graphs of
  two types of elements nodes and branches. The
  branches, which are electric components like
  resistors and voltage sources, connect the nodes,
  which can be viewed as representatives of voltage
  potentials.
• Circuit analysis is concerned with the
  computation of voltages and currents in a circuit
  for a certain excitation. There are various
  methods for equation formulation for a circuit.
  These are based on three types of equations found
  in circuit theory
• equations based on Kirchhoff's voltage law (KVL),
• equations based on Kirchhoff's current law (KCL),
  and
• branch constitutive equations.

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Basic circuit theory

• Solving a set of equations that represents a
  circuit is straightforward, if not always easy.
  However, developing that set of equations is not
  so easy.
• The two commonly taught methods for forming a set
  of equations are the node voltage (or nodal)
  method and the loop-current (or mesh) method.

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Basic circuit theory

• Conventions schematics
• While analysing a state of a circuit, one also
  writes the direction of current and the polarity
  of voltage in a schematic

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Basic circuit theory

• Marking voltage
• Technical and real direction of current

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Basic circuit theory

• Active and passive convention the elements
  within a circuit will either control the flow of
  electric energy or respond to it.
• Open and Closed Circuits
• 'Shorting' an element
• Kirchhoff's laws are expressions of conservation
  laws in physics, a conservation law states that
  a particular measurable property of an isolated
  physical system does not change as the system
  evolves. A partial listing of conservation laws
  that are said to be exact laws, or more precisely
  have never been shown to be violated.

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1st Kirchhoff (current) law - KCL

• Statement of the law of conservation of charge
  what goes in, must go out
• Or in particular the sum of currents going in
  and out of a given node, is always equal to zero.
  

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2nd Kirchhoff (current) law - KVL

• Statement of the law of conservation of energy
• The directed sum of the voltages (electrical
  potential differences) around a circuit
  (loop)must be zero.
• Sum of voltages around every closed loop in the
  circuit must equal zero. A closed loop has the
  obvious definition Starting at a node, trace a
  path through the circuit that returns you to the
  origin node.
• An element's voltage enters with a plus sign if
  traversing the closed path, we go from the
  positive to the negative of the voltage's
  definition.

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Ohms law and equivalence principle (Thevenin)

• Ohms law here is the branch equation for a
  resistor
• Equvalence principle - Thevenin theorem for
  resistive circuits, it is possible that circuits
  are represented through an equivalent circuit a
  black box

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Measurement

• Voltmeter is connected across two points,
  ampermeter is connected through a point

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Elementary electric circuit

• Simplest to solve using circuit theory
• Output voltage is simply equal to input voltage !

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Series connection the voltage divider

• Our basic circuit in this course.

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Series connection the voltage divider

• Our basic circuit in this course.

The input voltage E is divided in two
output voltages U1 and U2
The output voltage U2 is the input voltage
E, divided by
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Equivalent resistance of series connection

• What does the power supply E see?
• The equivalent resistance for resistors in series
  is, as a value, always dominated by the biggest
  resistor in the sum

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Parallel connection current divider
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Parallel connection current divider
The input current I is divided in two
output currents I1 and I2
-gt
The output voltage is the same as the input
voltage !
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Equivalent resistance of parallel connection

• What does the power supply E see?
• The equivalent resistance for resistors in
  parallel is, as a value, always dominated by the
  smallest resistor in the parallel combination.

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Combined connection
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Combined connection
To solve the circuit (find all the currents and
voltages, we must set a system of 6 equations,
using Kirchoff Laws and brach equations (Ohms
law).
The output voltage will be
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Combined connection
Easier way to solve the circuit
Find equivalent parallel resistance
And solve a voltage divider....
The output voltage will be
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Combined connection

• Important when Rih is almost infinite
  simulates a connection of a voltage divider to
  the data acquisition (Arduino)!

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Analysis methods

• Just a mention of two analysis methods for
  solving complicated circuits
• Node Voltage Method (Nodal analysis)
• Loop Current Method (Mesh current analysis)