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ELECTRICITY, BASICS, remember:
Qnt = Qmax (1 - e^-4)
63%
uF = x10^ …
ELECTRICITY
resistors in DC circuits
parallel circuit - closed circuit and current follows two or more paths
series circuit - closed circuit and current follows one path
combination circuit - parallel + circuit
junction - point in a circuit where three or more paths meet
loop - completed pathway around or part of a circuit
equivalent resistance - combined resistance of all components in a circuit
ohms law - electric current is proportional to voltage and inversely proportional to resistance
internal resistance - electrical resistance that limits the potential difference
kirchoffs current law - sum of all currents flowing into a node equals zero
kirchoffs voltage law - sum of all voltage drops and rises in a closed loop equals zero
potential difference - difference of electrical potential between two points
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inductors in DC circuits
eddy currents - loops of electrical current in planes perpendicular to the magnetic field, induced within conductors by a changing magnetic field
electromagnetic induction - the production of an electromotive force across an electrical conductor in a changing magnetic field
faradays law - a law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force
lenzs law - the direction of an induced current is always such as to oppose change in the circuit or the magnetic field that produces it
lorentz force - combination of electric and magnetic force on a point charge due to electromagnetic fields
inductance - causes an electromotive force because of a change in the current flowing
inductor - component in an electric or electronic circuit that possesses inductance
magnetic flux - total magnetic field which passes through a given area and is proportional to current change
primary windings - windings in a trransformer that carry the current/power from the original supply
secondary windings - transformer windings that have current induced in them by the changing magnetic field
isolating transformer - transfers power from a source of alternating current (AC) power to some isolated equipment or device
real transformer - lose a small amount of power due to resistance and eddy currents
ideal transformer - 100% efficient
step up transformer - output voltage higher than input voltage
step down transformer - output voltage lower than input voltage
RL circuit - circuit containing a a resistor and inductor connected to a power source
time constant (RL circuit) - time for the voltage or current to change by 63%
weber - unit for magnetic flux (o|)
henry - unit of inductance (H)
tesla - unit for magnetic field strength (B)
inductors + inductance
inductor: component in an electric or electronic circuit that possesses inductance
inductance: causes an electromotive force because of a change in the current flowing
we add inductors to DC circuits so that when a current is switched on or off the change is gradual rather than instant, this effect is due to the self-inductance (L) in the inductor and depends on:
- the number of coils
- the material of the core.
energy stored
- when a current flows through an inductor a magnetic field forms in which energy is stored, this is dependent on:
- size of the current
- self-inductance of the inductor
time constant (τ)
- time it takes for the current though an inductor to reach max depends on:
- self-inductance of the inductor
- resistance in the circuit
transformers
electrical devices made up of insulated wires on the primary and secondary coils, that use mutual inductance to change the voltage of a power supply = Np/Ns = Vp/VS
a changing current in the primary coil (AC supply) produces a changing magnetic flux that passes through the secondary coil - this induces a voltage in the secondary coil which creates a current in the secondary coil (efficiency and power = Vp Ip = Vs Is)
- step down transformer
- output voltage lower than input voltage
- fewer windings in the secondary coil which means that the voltage is decreased, current is increased to maintain the same power
- isolating transformer
- transfers power from a source of alternating current (AC) power to some isolated equipment or device
- same windings in the secondary coil which means that the voltage is the same, current is unchanged to maintain the same power
- step up transformer
- output voltage higher than input voltage
- more windings in the secondary coil which means that the voltage is increased, current is decreased to maintain the same power
AC circuits
angular frequency: the frequencyy of a steadily recurring phenomenon in radius per second, HZ --> angular frequency = x2pi
average power: half of the max AC power and equivalent to the DC power
capacitive reactance (Xc): how much a capacitor impedes or slow down the current in a circuit
frequency: the rate at which something occurs over a particular period of time
impedance: the effective resistance of an electric circuit or component to alternating current from the combined effects of resistance and reactance
in phase: when two or more waves or oscillations reach maximum and minimum values at the same time with the same frequency
inductive reactance: the opposition to a changing current flow caused by an inductor, measured in ohms - in inductors, voltage leads current by 90 degrees
instantaneous voltage/current: the voltage/current at any particular time when the voltage/current is continuously changing
lagging: following behind, as in current lags behind voltage by 90 degrees in inductors
leading: occurring before or in front of
peak voltage/current: the maximum voltage/current in a system where the voltage/current is continuously changing
period: the time taken for one oscillation to occur T =1/f
phase angle: a phase difference expressed as an angle, 360 degrees corresponding to one complete cycle
phasor: a line used to represent a complex electrical quantity as a vector
resonance: the increase in amplitude of oscillation of a system exposed to a force whose frequency is equal or very close to the systems natural frequency
resonant frequency: the natural frequency of oscillation of a system or object
RMS voltage/current: root mean square - the effective voltage/current of an AC wave
sinusoidal curve: a mathematical curve that describes a smooth periodic oscillation
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RMS (root mean sure)
- Imax = √2I rms
- Vmax = √2V rms
capacitors in AC
capacitive reactance (Xc = 1/2πfC = 1/ωC)
- reactance is dependent on frequency
- HIGH FREQUENCY: current is oscillating rapidly allowing the capacitor less time to charge meaning the current flowing around the circuit is impeded less by the capacitor and will have a smaller capacitive reactance
- LOW FREQUENCY: current is oscillating slowly allowing the capicitor more time to charge meaning the current flowing around the circuit is impeded more by the capacitor and will have a larger capacitive reactance
- will charge until the point that the voltage across the capacitor equals the supply voltage, however the size of the supply voltage is constantly changing (Vc >Vs)
- capacitor charging = Vs > Vc
- capacitor stops charging = Vs = Vc
- capacitor discharging = Vs < Vc
inductors in AC
reactance inductor reactance (Xc = 2πfL = ωL)
- reactance is dependent on
- HIGH FREQUENCY: current is changing rapidly so the inductor experiences a large change in magnetic flux which causes a larger induced voltage and more opposition to current flow - this creates a larger inductive reactance
- LOW FREQUENCY: current is changing more slowly so the inductor experiences a lower change n magnetic flux, this creates a smaller induced voltage and less opposition to current flow, there is a smaller inductive reactance
- the inductor in an AC circuit produced a continuously changing electric magnetic field to match the alternating current, this produces a back EMF opposing current
- inductor voltage VL is directly proportional to the current
- VL proportional I
- VL = XLI
resistors in AC
power in AC
P = IV
voltage and current are always in phase which means that power will never have a negative value
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BASICS
measurements
- charge on electron = -1.6 x10^-19
- charge on a proton = +1.6 x 10^-19
- charge (Q) = coulombs (C)
- resistance (R) = ohms (O)
- voltage (V) = voltmeters (V)
- work (W) = ?
- current (I) = amperes (A)
current (I)
- rate of flow of charged particles
- amps (s-1)
- current (I) = charge (Q) / time (t)
- I = Q/t
voltage
- how much energy there is per coulomb charge
- potential difference (P.D = V) is electrical energy being converted into something else
- electromotive force (EMF = V) is the something else being generated into electrical energy
- voltage (V) = current (I) x resistance (R)
- V = IR
- voltage (V) = energy (E) / charge (Q)
- V = E/Q
electric force (F)
- a complete circuit forms an electric field which drives the charge carriers within the circuit
- force (N) = electric field strength x charge (Q)
- F = EQ
work (W)
- energy (E) = electric field strength (NC^-1) x charge (Q) x distance (d)
- W = Fd = change in E
- change in E = Eqd
resistance (R) = (ohms)
- factors that effect resistance in a wire...
1) length (greater = increased resistance)
2) cross sectional area (greater = decreased resistance)
3) type of metal (resistivity of the material)
4) temperature (higher temp = greater resistance)
power (P)
- P = IV
- P = W/t
- the rate at which energy is changed by an electrical component.
- R (resistance)
- r (internal resistance)
- W (work)
- F (electric force)
- I (current)
- P (power)
- t (time)
- 3 (electromotive force)
- Vt (terminal resistance)
- L (self inductance) = Henry
remember:
- Qnt = Qmax (1 - e^-4)
- 63%
- uF = x10^ -6
- nF = x10^ -9
- pF = x10^ -12
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circuits
parallel
- current (I) IT = I1 + I2 + I3
- voltage (V) VT = V1 = V2 = V3
- resistance (R) 1/RT = 1/R1 + 1/R2 + 1/R3
series
- current (I) IT = I1 = I2 = I3
- voltage (V) VT = V 1+ V2 + V3
- resistance (R) RT = R1 + R2 + R3
V = Ed
E = qV
E = 1/2QV
CT = C1 + C2...
1/C3 = 1/C1 + 1/C2 + 1/C3
E = ½LI^2
t = L/R
XL = wL
V = IZ
w = 2-f
f = 1/T
- t = RC
- t = time constant (s)
- R = resistance (O)
C = capacitance (F)
- V = IR
- V = voltage (V)
- I = current (A)
- R = resistance (O)
- 3 = -Φ/t
- 3 = induced EMF (V)
- Φ = change in magnetic flux (Wb)
- t = change in time (s)
- Q = CV
- C = capacitance (F)
- Q = charge (C)
- V = voltage (V
- Φ = BA
- Φ = magnetic flux (Wb)
- B = magnetic field strength (T)
- A = area perpendicular to the magnetic field strength (m^2)
- Vt = 3 - IR
- Vt = terminal voltage (V)
- 3 = EMF (V)
- current (A)
- internal resistance (o)
- P = IV
- P = power (W)
- I = current (A)
- V = voltage (V)
- V = Ed
- V = voltage (V)
- E = ()
- d = distance (m)
- C = 3o3rA / d
- C = capacitance (F)
- 3o = absolute permivity of free space (8.84 X 10^14Fm-1)
- 3r = dielectric constant(unitless)
- A =overlapping area (m2)
- d = separation between plates (m)
- 3 = -L (ΔI/Δt)
- 3 = back emf (V)
- -L = self inductance (H)
- ΔI = current (A)
- Δt = time (s)
- τ = L/R
- τ = time constant (s)
- L = self inductance (H)
- R = reisstance (o)
- Np/Ns = Vp/Vs
- Np = number of turns PRIMARY
- Ns = number of turns SECONDARY
- Vp = primary voltage (V)
- Vs = secondary voltage (V)
- V = Vmax sin ωt
- V = instantaneous voltage (V)
- Vmax = maximum voltage (V)
- ω = angular speed (rad s-1)
- t = time (s)
- I = Imax sin ωt
- I = instantaneous current
- Imax = maximum current
- ω = angular speed (rad s-1)
- t = time (s)
- Imax = √2Irms
- Imax = maximum current
- Irms = rms current
- Vmax = √2Vrms
- Vmax = maximum velocity
- Vrms = rms velocity
- Xc = 1/2πfC = 1/ωC
- Xc = capcicatnce reactance (Ω)
- ω = angular frequency (rad s-1)
- C = capacitance (F)
- f = frequency (Hz)
- fo = 1/2π√LC
- fo = resonant frequency (Hz)
- L = inductance (H)
- C = capacitance (F)