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Electric Cicuites - Coggle Diagram

- - - - "Real" cicuits is made of a battery and almp. the construc of the circuit in the picture is the self-evident so it is a "real circuit
      - Portraying the essential function. Small signal circuit of a trnsistor. the network in the picture portrays the essential function of the device which in this case is a transistor.
      - Equivalent cicuits of a permenent magnet sunchronous machine. In this case there is no physical circuit but the functions of the machin can be reviewed with an equivalent circuit.
  - - - The unit of current is ampere, which is defined as:
        
        The current of one ampere in two conductors that are one meter away from and parallel to each other and are infinitely long and slim in a vacuum, causes a force of 2 x 10^-7 Newton.
        
        The positive direction of the current is the direction of the flow of the positive
        charge which is opposite to the movement direction of electrons.
  - - - Voltage: One volt is the potential difference (voltage) between two points when one joule of energy is used to move one coulomb of charge from one point to the other.
        
        While analyzing electric circuits, the potential difference, or more commonly known as voltage, is usually reviewed as well, the quantity being represented as u or U
        
        The positive direction of voltage is from the higher potential to the lower
        
        Electrical quantities as a function of time: alternating voltage and current.
        
        where û is the peak value of voltage and U the root-mean-square value, î is the peak value of current and I the root-mean-square value, ω the angular frequency, 𝜙𝑢 the zero-phase angle of voltage and 𝜙𝑖 the zero-phase angle of current.
        
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        Exponentially changing voltage and current, for example the
        charging/discharging current and voltage of a capacitor. where U and I are the initial values of voltage and current (t=0) and is
        the time constant
        
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  - - - If the circuit or the network contains only passive elements, there can’t
        be voltages or currents → the circuit is in hibernation.
        
        Potential differences and currents are formed when a source of electric energy is inserted in the circuit. The energy of the source transforms into heat in a resistor but in an ideal capacitor or inductor the energy is being either charged or discharged.
    - - Based off Kirchhoff’s voltage law, the total voltage of a series
        connection is the sum of the resistors’ voltage
        
        By dividing the total current of a parallel connection with the voltage U, the
        reciprocal of the resistance of the whole connection is
        
        Simplifying the circuit with wye-delta and
        delta-wye transformation. The transformations simplify the circuits in such way that the amount of equations to be solved diminishes
        
        Wye-delta transformation (Y-Δ): The wye interconnection has one joint point, the center junction point or the star point. In the delta interconnection the branches are connected from one node to
        another, no joint point
        
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    - - the waveforms of voltage and current as a function of time are in the same shape and in the case of the resistance, in the same phase.
        
        Direct voltage equals direct current and in the same phase alternating current equals alternating current.
    - - On direct current the capacitance has
        a charge but the current is zero. The voltage of the capacitance grows (capacitance equals an open circuit)
        
        Sinusoidal voltage equals sinusoidal current but as a function of time, they are not in the same phase. The current of an ideal capacitor leads 90 ° the voltage.
    - - On direct voltage the current of the coil grows (equals a short circuit)
        
        The current of an ideal coil equals the voltage but as a function of time, they are not in the same phase. The current lags 90 ° the voltage.
      - Mutual inductance M: If the magnetic field of wire (that has a changing current and magnetic field) reaches another nearby wire, emf (electromotive force) is induced in the second conductor
        
        This is what happend in transformers
  - - - A hibernating ideal voltage source doesn’t give a current or power when the circuit is open (picture a)
      - An ideal voltage source gives a current when the circuit is closed with a resistor (picture b)
    - - The ideal current source is in hibernation (its voltage is zero) when the
        source is short circuited, picture a
      - The ideal current source gets a voltage when a resistance R is added to the circuit, picture b
    - - DC Voltage Source = Ideal voltage soruce + internal resistanceRs in a seris (picture a). Thus the voltage of the source is:
        U=E-Rs*I
        
        DC current source = ideal current source + internal conductance 𝐺𝑠 in a series (picture a). Thus the voltage of the source is:
        𝐼 = 𝐽 − 𝐺𝑠*U
      - AC Voltage Sources = ideal voltage source + internal Indcutance Lz in a seris(picture b). Thus the voltage of the source is:
        u= e -Ls*(di/dt)
        
        AC current source = ideal current source + internal capacitance 𝐶𝑠 in a series (picture b). Thus the voltage of the source is:
        i = j-Cs(du/dt)
  - - - Voltage law: Sum of voltages rotating clockwise = Sum
        of voltages rotating counterclockwise
        𝑈1 + 𝑈2 + 𝑈3 + 𝑈4 = 𝑈5 or σ 𝑈 = 0
        In other words, sum of voltage sources =
        sum of voltage drops
      - Due to the linearity of the network the currents and volatages can be divided into componenets. Messh current and Node voltage methods
        
        The definition of the method the amount of meshses must be b - n +1.
        Where b = amount of the branches in the circuit
        n = amount of nodes in the circuit
        In other words these can be the windows.
        Directions can be freely chosen
        
        https://www.youtube.com/watch?v=j8LHrm3_brk
        
        Node-voltage method: This where we find the unknown volatges between the node points and the reference node.The reference node is selected as zero
        
        By applying Kirchhoff's volatage la, the voltages of the branches are derived fro, the voltage of the nodews points. Actual equations of the node=voltage method from the current components following Ohm's law under Kirchhhoff's current law
        
        https://www.youtube.com/watch?v=BMnFC63m1fQ
  - - - The current in any given branch of a multiple-source linear circuit can be found by determining the currents in that particular branch produced by each source acting alone
        
        Steps of theorem:
        Remoce all the othe sources only leave one
        Current sources can be replaced by opne cirucuit
        Voltage source can be raplaced by short circui
        Calculate the selected single source
        Calculate the next source (repeat same for all)
        Combine all the results
        
        Divide currents into components generated by voltage sources E1 , E2 and E3
        
        To calculate the component I11 generated by E1 the other voltage sources E2 and E3 are shorted → A one-source circuit
        
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        Voltage components generated by the ideal current
        sources:
        
        To calculate the component U11 generated by J1 the other current sources J2 and J3 are opened → A onesource circuit is derived
        
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    - - ET is the same voltage that affects between the points A and B before any branch is connected between them (idle voltage U0)
        
        RT is ET divided with the current Ik which flows trough
        points A and B if they are shorted (short-circuit current)
        
        When the Thevenin’s source is formed the current in the new
        attachable branch is
        
        → Method particularly useful when the circuit remains unchanged but the resistance Ra of the attachable branch changes
        
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    - - Jn is derived by shorting the branch and measuring / calculating the short-circuit current
        
        Gn is derived from the conductance of the original circuit or
        
        GN is also derivable by opening the shorted branch and measuring / calculating the idle voltage
        
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- - - - So, the average of AC period is 0. If not, the current is said to have a DC component (mixed current)
        
        The DC component is calculated as a time average
        
        An important special case: sinusoidal alternating current
        Instantaneous value
        
        î is the peak value or amplitude
        f is the frequency of the current (reciprocal value of
        period, f = 1/T)
        During one period T the argument of the sinusoid grows
        360° = 2 rad
        
        The average rectified value of alternating current equals the direct current which during one period transfers an equally large charge as the ac rectified
        
        Let’s inspect the direct current Imed, which is the amount of
        the AC average rectified value i = f (t)
        
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        ROOT MEAN SQUARE (RMS): The rms value of a sinusoidal current is equal to the dc current that produces the same amount of heat in a resistance as the sinusoidal current does.
        
        I dissipates heat energy in resistance R
        
        The sinusoidal current (ac) i dissipates heat energy in time dt
        
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        FREQUENCY AND ANGULAR FREQUENCY: If the coil rotates at speed  the magnetic flux flowing through it alters cosinusoidally
        
        Where 𝜙෠ is the peak value
        
        According to Faraday’s induction law the shifting of the flux generates a source voltage in a coil with N loops
        
        As unloaded the terminal voltage is u = e
        
        If the coil rotates once (360° = 2 rad) in time T is
        
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        Calculating AC circuits: Calculation of AC is different to DC, this is because of the addition to values of the quantities the frequency and phase shift must also be taken intto account.
        
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    - - RESISTOR: There are many application for resistances, sometimes the goal is to make the resistance as small as possible, other times the goal is to achive a specific resistance.
        
        Each material has a specific resistance depending on the temperature. Whne the specific resistance (ρ), cross-sectional area (A) and the length of the wire are known the resistance can be calculated from the equation
        
        Types of resistors:
        Mass resistors: Ros is a misture of coal and quartz. Cheap and reliable, weak stability
        Film resistors: A thin film of coal or metal deposited onto a ceramic rod. Better stability than the mass resistor, weak mechanic durability
        Wirewound resistors: Resistive wire wound around an insulating rod. Good power rating and accuracy. Parasitic cicuit elemets
        Variable resistor: Potentiometers and trimmers. Linear and logarithmic.
        Thermsistors: NTC/PTC (Negative/Pozitive temperature coefficient)
        
        Parasitic circuit elements of resistors. The wire also froms a coil with a certain inductance. Potential difference between the wrie loops and thus a certain capacitance. So resistor isn't an ideal component containing only resitance. If necessay to analyze the functions on different frequencies, the resistor must be replaced with an equivalent connection
        .
        On the frequency, the resistor is mean to be used, the sufficient accuracy is R>>L, R>>C => Z=R
        As the frequency grows the affliction of inductance grows first, then of the capacitance. The resistance also grows due to the skin-effect
        
        The inductance of the wirewound resistor can be diminished by wounding the consecutive loops in opposite directions. The inducatnce can also be diminished by using a straight resistor rod or a tube-like structure.
        To keep the capacitance small the loops in the opposite ends must not be close
      - INDUCTION COILS, AIR CORE: Same equivalent connection as to the wiredwound resistor, but on the using frequency it;s almost purely inductance.
        Resistance is diminished by using iwres with a large enough cross-sectional area.
        
        Alternating current flows best close to the surface of the wire (skin effect). On a samll frequency the induction coil can be portrayed as a series connection of inductance and resistance.
        
        With a big enough frequency, the influence of the resistance is insignificant but the capacitance between the loops is significant. The equivilant circuit is a parallel connection of inductance and capacitance.
        
        INDUCTION COIL, IRON CORE: The inductnace of air cored coil is relitively small. A bigger inductance is achived whne the coils are wound around an iron core.
        Iron core causes nonlinearity into the inductance, an air gap linearizes the behavior. Usually, the iron core is made of slim, insulated plates to diminish the iron losses genereated by the shifting magnetic field
        
        The iron loses are taken into account by the parallel resistance Rr. The "Copper losses" forming in the wires are portrayed by the series resistance Rs. Usually assumed that Rr>>Rs
        
        Loss factor
      - CAPACITORO: Air insulated capacitors can't withstand high voltages. Usually an insulating material is used.
        The dielectric insulating materials cayses power losses due to the shifting of the polarization.
        
        Power losses are taken into account by a parallel resistance. Additionally the wires and connections contain a small resistance and inducatnce.
        
        The losses forming in a capacitor are portrayed by the loss factor
        
        A capacitance and a voltage withstading are given to the capcitor.
        Capacitro types:
        
        Electrolytic capacitors (high capacitance values, power supply filtering)
        
        − Ceramic capacitors (small, cheap, non polarized, decoupling & filtering)
        
        − Plastic-film capacitors (audio and high frequency applications)
        
        − Mica capacitors (high performance, RF circuits, high power systems)
        
        − Super capacitors (high capacitance, energy storage and backup power)
        
        − Variable capacitors (air or plastic insulated)
    - - The are three phases in a symmetric system wiht one third of a period (120) phase shift each. The sum of the phase voltages (instantaneous values/ phasors) is zero
        The phase are marked wiht number or letter: L1, L2, L3, or R, S, T
        
        While analyzing the power it was noticed that the power alternates at a twice as large frequency as the alternating current.
        
        In the three-phase system the elements shifting with time are nullified. The transfer of power is consistent and the transfer losses smaller. It can easily be established a rotating magnetic field which allows the usage of simple electric machines.
        
        The sum of the current and voltages is zero in balanced (or symmetrical) three-phase system. This, no neutral wirre is needed in addition to the phase wires. Savings in the materials and pirces of the powerlines.
        
        PRODUCING THREE PHASE VOLTAGE: in a balanced three phase systme. Source voltages iduce into the coils. There is a 120 phase shift between teh phases. As a result the three phase voltages is symmetric.