Please enable JavaScript.

Coggle requires JavaScript to display documents.

Engineering Mechanics , Engineering Physics, Electrical Engineering -…

- - - - Normally force are ditributed along the structure, but can be simplified into a point
        
        To do this we use Integrals
        𝑭𝑹 = Integral(𝒘(𝒙)) 𝒅𝒙
    - - These can be broken down into X and Y components. Then use trig to find the resultant
  - - - Right hand rules
      - If the force is parraller to the line of action then the moments is 0
        M=Fd
        M=F*0
        M=0
  - - - The resultant force being 0 means that the particle is not experiencing any acceleration. This could mean that the object is not moving or that he object is moving at a constant velocity.
        
        A free body diagram is used to see cleary where are all the forces coming from and how they are interacting with the particle.
        
        useful applications
        
        This can be used to analyze knots, pulleys, connecting rings, and any small detail where all forces acting on it can be described as
        acting on its center
        
        These analysis often requie us to look at tension on string and forces on spring. So it good to also know Hook's law, F=kx
        
        Opposed to this, larger objects (beams etc) can not be represented as particles. This kind of objects are called rigid bodies
  - - - With kinematics, there are four main variables that we will be working with. Velocity, displacement, time and acceleration.
        The relations between these quantities are described as time derivatives
        
        v = dS/dt
        a = dv/dt = d2S/dt^2
        a ds = v dv
    - - In these cases, both our velocity and acceleration become Pythagorean products
        of their x- and y-components, so their magnitudes are:
        
        Direction angles can be calculated from x- and y-components using inverse
        tangent:
        
        The most common application for this would be for projectiles but the (x,y)-component method works well for cases, where the curvilinear nature of motion is a product of things happening in both directions – i.e. the motion must not be curvilinear by definition
      - If our situation is different in such a way that the curvilinear nature is forced because of our particle is moving along a path that is known beforehand, then it is usually simpler to perform our calculations in a plane which consists of normal and tangential components (n and t)
        
        Here at represents the acceleration caused by change in the magnitude of the velocity and an represents the acceleration caused by change in the direction of the velocity
        
        Tangential and normal components of the acceleration can be easily calculated
        using the following formulas
        
        Tangential acceleration is the time derivative of velocity
        
        Normal acceleration is velocity squared
        and divided by radius of curvature ρ
        
        1 more item...
      - Third possible coordinate system that we can use is the system of cylindrical coordinates (or, in plane, polar coordinates r and θ )
        
        This is useful in applications where our particle moves at certain angular velocity, The radius of the path of our particle changes respect to time
        
        Very common in machine design:
        Slider-connecting rod –mechanisms
        Robot arm movements
        
        In polar coordinates, our velocity equation takes the form
        
        • Likewise, our acceleration equation takes the form
        
        1 more item...
        
        Note:we often use dots to imply time (t) derivatives
- - - - Charge – detection using an electroscope
  - - - I = ∆q/∆t
        
        The rate at which electrons flow past a point in a complete electrical circuit.
    - - electric charges experience the electric force, when one charge is moved in the vicinity of another, work W is done
        
        V = W/q
        
        when speaking about individual charges, electronvoltts is used instead if joules as it the value is very small
        
        w=deltaVq
        1 eV= eV= 1.610^-19 q 1 V
    - - Assuming the charge carriers in a conductor are free to move, if a conductor is suddenly accelerated, the electrons would “pool” at the trailing side due to inertia, and a potential difference measured by a voltmeter would be set up between the ends.
        
        In a metal, free electrons move very rapidly, but collide constantly with the atoms in the crystalline lattice
        
        Note that through any cross-section of the conductor, the net current is zero
        
        If we place that same portion of conductor under the influence of a potential difference, we have a slow drifting of the velocities toward the lower potentia
        
        Note that the net current is NOT zero in this case.
        ∙The electrons still have a high velocity, but this time the net migration is in the direction of the lower potential.
        ∙The speed of this net migration is called the drift velocity.
        
        I = nAvq
        
        v is the drift velocity
        A. is the area of the wire
    - - r is the distance between th origins of two circles
      - Electric field
        
        E = F/q
        
        Electric field – the field model
        
        Coulomb force signal cannot propagate faster than the speed of light, electrons trapped in orbits about nuclei cannot instantaneously feel the Coulomb force, and thus cannot instantaneously adjust their motion on time to remain in a circular orbit
        
        Electric field – sketching
        
        2 more items...
    - - Some very precise resistors are made of wire and are called wire-wound resistors.
        
        Resistance is measured in ohms (Ω) using an ohm-meter.
        
        R = V/I
        
        Resistance can be affected by. the area and the length of the wire
        
        ρ = RA/L
        
        ρ means the resistivity of the material
        
        non ohmic behaviour
        
        The temperature coefficient for tungsten is positive, typical for conductors. Therefore, the hotter the filament the higher R. But the more current, the hotter a lamp filament burns. Thus, the bigger the I the bigger the R.
        
        This is why a lamp filament might not have an ohmic behaviour, because of the change in temperature
      - ∙And some resistors can be made to vary their resistance by tapping them at various places. These are called variable resistors and potentiometers.
      - ∙Thermistors are temperature- dependent resistors, changing their resistance in response to their temperature.
      - ∙Light-dependent resistors (LDRs) change their resistance in response to light intensity.
    - - P = VI = I^2R = V^2/R
    - - Investigating combinations of resistors in series
        
        ammeters are connected in series
        
        To measure the current of the circuit we must break the circuit and insert the ammeter so that it intercepts all of the electrons that normally travel through the circuit
        
        An ideal ammeter how infinitely zero resistance
      - Investigating combinations of resistors in parralel
        
        voltmeters are connected in parallel
        
        To measure the voltage of the circuit we merely connect the voltmeter while the circuit is in operation
        
        An ideal voltmeter has infinite resistance
      - Potential divider circuits
        
        A potential divider is a circuit made of two (or more) series resistors that allows us to tap off any voltage we want that is less than the battery voltage
        
        The input voltage is the emf of the battery.
        The output voltage is the voltage drop across R2.
        Since the resistors are in series R = R1 + R2.
      - Kirchhoff’s rules
        
        ”Solving” a circuit consists of finding the voltages and currents of all of its components
        
        STEP 1: Assign a current to each branch. If you have a good idea which way it flows, choose that direction.
        If you don’t, an arbitrary direction will do just fine
        
        If a current enters a junction it is a “gain” and is assigned a POSITIVE value. If a current leaves a junction it is a “loss” and is assigned a NEGATIVE value
        
        For the TOP junction, I1 and I3 are both POSITIVE and I2 is NEGATIVE.
        For the BOTTOM junction, I1 and I3 are both NEGATIVE and I2 is POSITIVE
        
        STEP 2: Use Kirchhoff’s rule for I for each junction.
        Each JUNCTION yields its own equation
        
        1 more item...
        
        key terms
        
        A junction is a point in a circuit where three or more wires are connected together.
        
        ∙A branch is all the wire and all the components connecting one junction to another.
        
        ∙A loop is all the wire and all the components in a complete circle
      - Capacitors in parralel
        
        You add the capacitance
      - Capacitors in series
        
        You add the inverses of the capacitances
    - - A capacitor is a passive electronic component that stores
        electric charge.
        Unit Farad
        
        Capacitors store charge between two conductive plates separated by a dielectric material
        
        Factors that affect capacitance are distance (d), area of the plates (A), and the dialectric constant
        
        When the capacitor charges, the current on the capacitor decreases exponentialy. When the capacitor is discharged, the current flows to the other side and then decreases (or a i guess increases) exponentialy again.
        
        2 more items...
        
        The Formula for when the dialectric isn't a vacum is C=εA/d.
        where ε=kε0
      - Common capacitors
        
        Ceramic Capacitors: These are widely used due to their
        small size, stability, and ability to handle high frequencies.
        
        . Electrolytic Capacitors: Known for their larger capacitance
        values, these are often used in power supply circuits.
        
        . Film Capacitors: Valued for their reliability and precision, these are used in applications requiring stable and accurate capacitance
  - - - Electromagnetic force (also Lorentz force):
        𝐹 = 𝑞𝐸 + 𝑞𝑣⨯ 𝐵
        If you noticed the firest hald of the equation is the electric field strength equation and the second half is the magnetic force equation
        
        Magnetic flux density B. s the number of
        magnetic field lines passing through as surface, the magnetic flux density B, is the flux Φ per area A.
        If the are is at another angle than 90 degrees towards the flux: Φ = B A sin (𝜃)
        
        Magnetic fieald strength H, H is a measure of the intensity of the magnetic field in a given area of tha field. It depends on the density flux and the permeability of the medium 𝜇:
        H = B/ 𝜇
        
        Here 𝜇𝑟 is the relative permeability and 𝜇0 the permeability of vacuum
        Note: while analogous, permeability is not to be confused with [electric] permittivity (ε), which describes a medium’s property to store energy in the form
      - Typical cases
        
        Electrical charge moving in a magnetic field:
        𝐹𝑚 = 𝑞𝑣𝐵 𝑠𝑖𝑛(𝜃)
        
        Conductor (length l ) carrying a current (i) in a
        magnetic field:
        𝐹𝑚 = 𝑖𝑙𝐵 𝑠𝑖𝑛(𝜃)
        
        Torque on a [conductor] shaft in a magnetic
        field:
        𝑇=𝑟 𝐹𝑚 𝑠𝑖𝑛
        
        For all of these don't forget the arrow rules, croses means that the magnetic field is going into the page and dots means it's going out of the page
        
        Also right hand rule
        
        1 more item...
  - - - Importantly for many applications, the voltage induced in a conductor loop, V (also ε), is given by Faraday’s law:
        𝑉= -𝑑𝝫/𝑑𝑡 (rate of change of flux
        There is also flux linkage which is just flux (𝝫) times the number of loops
        
        Inductor
        
        Inductor is based on the magnetic field that forms when the current flows through a loop or a coiled conductor. Both charging and discharging an inductor takes some time, making it a dynamic component
        
        The total self inductance of a solenoid type inductor can be defined as a function of cross-section area 𝐴 and number 𝑁 of the loops in it and the total length ℓ it has, as well as the permeability of the medium at the core 𝜇:
        𝐿 = (𝜇0 𝑁^2 𝐴)/ℓ
        
        Don't forget about faraday's law, here when the flux is increasing, the coil creates a emf that opposes that increase in flux.
        The resistance to this change in current/ flux is called self inductances
        
        This opposing action is also why faraday's law has a negative sign
        
        1 more item...
        
        Voltage Transformers
        
        We explore the concept of step-up and step-down transformers in
        power grids: what are the voltage transformation ratios. tranformer also cause mutal induction as change in current causes change in current in another coil
        
        These are all the formulas to convert anything between to transformers.
        
        For the relation ship between emf and voltage it makes sense, the more loops, the higher the flux linkage and the higher the voltage
        
        1 more item...