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Engineering Physics, Engineering Physics - Coggle Diagram

- - - - 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
        
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    - - 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
        
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        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.
        
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        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
        
        𝜇 = 𝜇0 * 𝜇𝑟
      - 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
        
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  - - - 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
        
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        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
        
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- - - - Period = 1/ frequency = 2π / ω
  - - - Force on an object on a circular path that keeps the object moving on the path. It is always directed towards the center and its magnitude is constant
        
        To find angular velocity, desplacment and acceleration. you have to divide it by the radius
  - - - a = -ω2x
        
        x=x0 cos ωt OR
        x=x0 cos θ
        
        This equation set works only for a mass which begins at x = +x0 and is released from rest at t = 0 s.
        
        v = -x0 sin ωt and v0 = x0ω
        
        x2 = x02 cos2 ωt,
        v2 = (- x0ω sin ωt)2 = x02 ω2 sin2 ωt.
        so that v2 = x02ω2(1 – cos2 ωt) or v2 = ω2(x02 – x02 cos2 ωt).
        ∙Now sin2 ωt + cos2 ωt = 1 yields sin2 ωt = 1 – cos2 ωt
        ∙Then v2 = ω2(x02 – x2), which becomes
        
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      - a is directly proportional to -x
    - - The first total energy formula wont work if the sin or cos is shifted
    - - The propegation can happen in matter/ medium or in the distrubance of electromagnetic waves. The speed of these waves depend on the medium but for electro magnetic waves, it always travels at the speed of ligth
        
        MECHANICAL WAVES: a wave that is not capable of transmitting its energy through a vacuum. Mechanical waves require a medium to transport their energy from one location to another.
        There are two types of waves, transverse and longitudinal waves.
        
        TRANSVERSE WAVES:when the particles vibrate perpendicular to wave energy movement
        
        Speed of wave propegation:
        
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        LONGITUDINAL WAVES:When the particle vibrate parallel to the
        movement of energy in a wave.
        
        ELECTROMAGNETIC WAVES: Electromagnetic waves are fluctuations in the electromagnetic field. They do not require a medium to propagate; Speed of propagation c = 3*108 m/s;
        
        Wave consists of electric field (“E”) and amagnetic field (“H” or “B”) components, that are at 90-degree angle (right angle) both to each other and the axis of propagation
        
        Maxwell’s equations encompass the major laws of electricity and magnetism.
        
        Electric field lines originate on positive charges and terminate on negative charges. The electric field is defined as the force per unit charge on a test charge, and the strength of the force is related to the electric constant , also known as the permittivity of free space
        
        Magnetic field lines are continuous, having no beginning or end. No magnetic monopoles are known to exist. The strength of the magnetic force is related to the magnetic constant , also known as the permeability of free space. This second of Maxwell’s equations is known as Gauss’s law for magnetism.
        
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        DIFFRACTION: When a planar wave front encounters an obstacle where only a short part of the wave front can pass, the wavefront changes shape towards a spherical wave front
        
        THE HUYGENS PRINCIPLE: In 1678 Huygens proposed a model where each point on a wavefront may be regarded as a source of waves expanding from that point. Each point of a wave front can be considered as a center point of circular wave for the next wave front
        
        DOUBLE SLITS: Interference takes place when waves travel a different distance (r1, r2) from nearby slits in the obstacle. Superposition: sum of the waves in different phase φ, interference can be constructive or destructive, depending on Δr
        
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- - - - Internal energy: 𝑈 of a thermodynamic system is the energy contained within it. Includes the energy contained in the movement of particles in the system and their chemical bounds.
        
        Does not include the kinetic energy of the system as a whole.
        Does not include the potential energy of the system
        
        Conservation of energy: Energy can be transformer from one form to another, but the total quantity remains constant
        
        The slides also mention gravetational potential energy as well as kinetic energy
        
        THERMAL EXPANSION: Thermal expansion is dependent on the state of the matter. Expansion is fastest in gases and slowest in solids.
        
        Thermal expansion of solids often results in quite linear change in the length of the solid, assuming the change in temperature remains small.
        Assuming 𝐿0 is the length of solid before temperature change, the length after temperature change Δ𝑇 is
        
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    - - 𝑅u – universal gas constant = 8.134 J/(mol K)
        𝑀 – molar mass of the gas
        𝑁 – amount of gas in moles (mol)
        
        Universal gas constant can be replaced with substance specific gas constant. Substance specific gas constant is related to universal gas constant
        
        f bodies A and B are each in thermal equilibrium with a third body T, then A and B are in thermal equilibrium with each other.
        More accurately the amount of pressure 𝑝 is the average perpendicular force 𝐹 effecting a surface area 𝐴, so 𝑝 =
        𝐹/𝐴, while 𝑝 = Pa = 𝑁Τ𝑚2
        
        Specific heat capacity: thermodynamic property of a material which entails the amount of heat required per unit mass to raise the temperature of one-degree Celsius
        
        Work is the energy transferred to or from an object via application of force. Using a constant force 𝐹, the work 𝑊 done to an object can be calculated by considering the achieved displacement
        𝑠 of the object
    - - Temperature 𝑇 is a statistical quantity, that is defined based on the average kinetic energy of particles. There is a lower limit, however : when there is no heat movement of the particles, the system has reached the absolute zero temperature,
        𝑇0 = −273.15℃ = 0 K
        
        In a closed system, temperature differences balance out when enough time has passed . This is called thermal equilibrium
        
        THE ZEROTH LAW OF THERMODYNAMICS: If bodies A and B are each in thermal equilibrium with a third body T, then A and B
        are in thermal equilibrium with each other.
    - - THERMAL CONDUCTION: Heat transfer through physical contact of objects (or gases and fluids). Always from higher to lower temperature
        
        Magnitude of heat transfer (Q/t) by conduction depends on:
        Contact surface area, A
        Thickness of surface, d
        Temperature difference ΔT
        Thermal conductivity of the material, k
        P is the power or rate of heat transfer in watts or in kilocalories per second
        
        Conduction through a (layered) composite material: if no heat is stored or generated, the heat flux (Q/t) through all the components is the same.
      - THERMAL CONVECTION: Heat transfer through movement of fluid. Requires movement or exchange of mass.
        Always from higher to lower temperature. Heat can transfer as internal energy stored (in the fluid’s molecules’ movement, as sensible heat) or via phase changes (latent heat).
        
        The amount of buoyancy is dependent on the density of the fluid. Denser or cooler fluids have less kinetic energy than more excited fluids, so they exert less pressure against other surrounding molecules. Since there is less pressure generated by this fluid, the force of gravity has more effect on this fluid than warmer fluid
        
        Heat transfer coefficient, h
      - RADIATION: Heat transfer though radiation (emitted or absorbed). No physical contact or medium is required. All objects absorb and emit electromagnetic radiation. The rate of heat transfer by radiation is largely determined by the
        color of the object.
        
        Magnitude of heat transfer (Q/t) by radiation depends on:
        Surface area of object A
        Emissivity, ε. An ideal black body radiator has ε = 1, whereas a perfect reflector has ε =0.
        Temperature T
        Stefan-Boltzmann constant σ = 5.67 × 10^−8 J/s · 𝑚^2· 𝐾^4
        
        The rate of heat transfer by emitted radiation is
        described by the Stefan-Boltzmann law of radiation:
        
        Heat transfer for an object (o) and its environment (e):
      - GREENHOUSE EFFECT: The Earth’s relatively constant temperature is a result of the energy balance between the incoming solar radiation and the energy radiated from the Earth.
        
        The atmosphere, like window glass, is transparent to incoming visible radiation and most of the Sun’s infrared. These wavelengths are absorbed by the Earth and re-emitted as infrared.
        
        The atmosphere, like glass, traps these longer infrared rays, keeping the Earth warmer than it would otherwise be.
        
        Greenhouse gases (GHGs) are the gases in the atmosphere that raise the surface temperature of planets such as the Earth
      - STATES OF MATTER: we are familiar with the main three state of matter, solid liquid and gases. As well as how their structure look like and the names of the their transition states
        
        PLASMA: This is reffered as the 4th state of matter. It consists of a hot, ionized gas with roughly equal numbers of positively charged ions and free electrons.
        
        Its formed by highvoltage and extreme temperature, which is what separate the electrons from its atom. For plasma we use physics and kinetic theory to understand and model it complex dynamic instead of traditional thermodynamics, as its not enought to describe its behavior
        
        ExamplesL lightining, electric sparks, Aurora
        
        HEAT QUANTITY IN PHASE TRANSITION: To evaporate matter, a significant amount of energy is required. The same energy is released, when the matter condensates back to liquid.
        
        Both the latent heat of evaporation (also enthalpy of evaporation) and latent heat of fusion (also enthalpy of fusion) carry the symbol of heat quantity 𝑄 and the amount of heat can be calculated using the specific heat of evaporation 𝑠 and specific heat of fusion 𝑟 as below
        
        THe m is the mass of the matter in question
        
        PHASE DIAGRAM: Phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. A typical phase diagram has pressure on the y-axis and temperature on the x-axis. As we cross the lines or curves on the phase diagram, a phase change occurs.
        
        In addition, two states of the substance coexist in equilibrium on the lines or curves.In addition, there is the supercritical area at high pressure and temperature. The critical point defines the entry to supercritical region, where evaporation is not a clear transition anymore.
        
        PHASE DIAGRAM OF WATER: For example, the boiling point of water is 100oC at 1.00 atm. As the pressure increases, the boiling temperature rises steadily to 374oC at a pressure of 218 atm.
        
        A pressure cooker (or even a covered pot) will cook food faster because the water can exist as a liquid at temperatures greater than 100oC without all boiling away. The curve ends at a point called the critical point because at higher temperatures the liquid phase does not exist at any pressure
        
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  - - - The change of total energy in a system is a sum of the work and heat quantity it has received.
        Δ𝐸𝑡𝑜𝑡 = 𝑊 + Δ𝑄
        In thermodynamics the change typically happens in the internal energy of the system, resulting in
        Δ𝑈 = 𝑊 + ΔQ
        
        HEAT ENGINE: A heat engine is a device used to extract heat from a source and then convert it into mechanical work that is used for all sorts of applications.
        
        In A Heat Engine, part of the heat from a source 𝑄𝐻
        can be converted into work 𝑊. Its efficiency is:
        
        The theoretical maximum efficiency of a heat engine can also be solved using the temperature of the hotter heat source 𝑇1 and the temperature at the heat cycle exhaust point 𝑇2
        
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        INVERSE HEAT ENGINE: Devices that transfer heat from a cooler area to a warmer area, using work.
        
        Now, different performance indicators are used for
        refrigeration (cooling) and heating using heat pumps
        
        For refrigeration, we have a coefficient of performance
        (CoP) as
        
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