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Section 1. Definitions
1 Gravitational field
Newton's law of gravitation
gravitational attraction force between twopoint or spherical massesisproportional to product of massesandinversely proportional to square of separation
Gravitational field strength
gravitationalforce per unit mass
Gravitational potential
work done per unit masswhile moving a test massfrom inifinityto a specific point without changing its velocity
What is meant by a field of force?
a region in space where an opbject experience a force
2 Circular motion
Angular frequency
rate of change of angular displacement
in SHM, angular frequency is 2pi*frequency
Radian
consider an anlge suited in a circle, radian is theratio between the arc length subtended by the angle to the radius of circle
3 Thermodynamics
Specific latent heat
energyper unit massrequired tochange the stateof an objectat constant temperature
Specific heat capacity
energyper unit massrequired to increase the temperature of an object by 1 degreewithout changing its state
Internal energy
sum ofpotential and kinetic energydue to therandom motion of molecules
Avogadro constant NA
number carbon-12 atoms in 12 g of carbon-12
Mole
isunit of amount of substancethat contains the number of 6.02*10^23
Delta_U: increase in internal energy
q: heat transferred to system
w: work done on system
4 Electromagnetism
Magnetic field
region in space where amagnet, magnetic material and current-carrying conductorsexperience forces
Coulomb's law
electric force between twopoint or spherical chargesisproportional to product of chargesandinversely proportional to square of separation
Capacitance
charge per unit potential differenceacross a capacitor
Tesla
unit of magnetic flux densitythat is normal to a long wire carrying a current of 1A that creates a force of 1N/m
Faraday's law
induced emfis proportional to therate of changeof magneticflux linkage
5 Quantum physics
Photoelectric effect
electromagnetic radiation with sufficient frequencyincident on the surface of metal
will causeemission of electrons from the metal surface
Threshold frequency
minimum frequencyabove which incident light will be able toexcite photoelectrons emission from metal surface
Photon
is apacket of energyof electromagnetic radiation
de Broglie wavelength
wavelength associated with a moving particle realted to its momentum
6 Nuclear physics
Radioactive
unstable nucleuswill emitionising radiationrandomly and spontaneously
Decay constant
probabilityof a nucleus to decayper unit time
Half-life
timefor number of nuclei or activity to become half
Section 2. Circular motion and gravitational field
Why thegravitational field strengthmay be considered to beconstant near Earth's surface?
g=GM/R^2 --> g=GM/(R+h)^2
so in change in height is much less than radius of Earth then g remains constant
Why isgravitational potentialanegativequantity?
gravitational potential is defined to be zero at inifinity
in moving a mass from infinity to a point, work done is always negative because gravitational force is always attractive, by definition of gravitational potential, negative work means potential is negative
Feature ofgeostationary orbits
period of 24 hours
orbits right above the equator
at fixed orbital distance
orbiting earth from west to east
How satellites stay in circular orbits around planets?
planet exerts gravitational attraction force on satellite
this gravitational attraction hasconstant magnitudeand isalways perpendicualr to satellite velocity, so itprovides the centripetal force
Section 3. Simple harmonic motion
Explain how an expression can show that object will undergo SHM
magnitudeof resultant force (or acceleration) on the object isdirectly proportional to displacementwith constant proportionality
directionof resultant force (or acceleration) is always opposite to direction of displacement
Forced oscillations
Difference betweenfree and forced oscillations
Free oscillation
oscillationswithout any external forcesapplied
sono loss of energyorno damping
sono driven forcesoamplitude does not increasedue to resonance
Forced oscillation
oscillations withcontinuous energy inputprovided by externalperiodic driving force
Resonance
whendriving forcehas frequency matches thenatural frequencyof oscillator
resonance happens and oscillatorabsorb external energy very fastand grow tomaximum amplitude
Damping
when externalresistance forcesact on oscillator
results incontinuous decrease in energy and amplitudeof oscillation
Section 4. Thermodynamics
1 Temperature and internal energy changes
What may be deduced from the difference in temperatures of two objects?
temperature determines thedirection and rateof transfer of thermal energy between objects
What is the basic principle by which temperature is measured?
a property of a substance that chages with temperature
What is meant by saying that two bodies are inthermal equilibrium?
two bodies areat the same temperatureand ther isno net energy transferbetween bodies
Describe what is observed when viewingBrownian motionunder microscope
specks of lightreflected from pollen grainsdue to the random vibrationof the pollen grain
There are two types of thermometers
Thermocouple
robust
very wide range
small size so small thermal capacity so act fast to change in temperature
high sensitivity
non-linear so requires calibration
Thermistor or resistance wire thermometer
robust
narrower range for thermistor, wide range for resistance wire
bigger size so big thermal capacity so act slower to change in temperature
high sensitivity for thermistor (but narrow range), low sensitivity for resistance wire
linear for both thermistor and wire
2 Ideal gases
Assumptions of ideal gases
Forces between particles are negligibleexcept during collisions
so thatpotential energybetween molecules can be assumed to bezeroandinternal energy is entirely kinetic energy
Volume of particles is negligiblecompared to volume of gas
Frequency of collision is lowso that time between collision is longer than time during collisions
Collisions areperfectly elasticso no kinetic energy is lost
Number of particles is large
so that statistics can be applied to analyse molecules population
Describe motion of molecules in a gas according to the kinetic theory
gas molecules move withrandomly distributed speed and direction
gas molecules havezigzag trajectoriesdue tocollisions between molecules
Section 5. Communication
1 AM/FM
Amplitude modulation
amplitude of carrier wave varies with the displacement of the information signal
Frequency modulation
frequency of carrier wave varies with the displacement of the information signal
2 Analogue and digital signals
What is meant by digital signal?
discretesignal that consists of a series of1 and 0
What is meant by analogue signal?
signal thatvaries continuouslywith time
Analogue to digital convertion
What is the effect ofsample frequency?
increase sample frequency will reduce width of digital signal
sofastchanges in input signal can be reproduced
What is the effect ofstep size?
decrease step size will reduce step height
sosmallerchanges in input signal can be reproduced
Advantage of digital signal compare to analogue
it is possible toregeneratedigital signal
so that noise can be eliminated completely and original signal can be recovered
digital signals can be turnedfrom parallel to serial
so that reduced line of channel
more secure due to encryption
possible to check error when extra bit is added
What is meant by regeneration?
noise is removedfrom the signal
so that the original signal can be recovered
Definition ofattenuation
gradualloss of intensity or amplitudeof signal
Why an analogue signal cannot be regenerated?
in analogue signal the superposednoise cannot be distinguished from the signal
so when signal is amplified,noise will be amplified too
Describe functions of ADC
taking samples of analogue signal at regular intervals
and converting the analogue number to a digital number
Advantages of optic fibre compared to metal wire

greater bandwidth
less interference and noise
less cross-talk
less attenuation
less weight and cheaper
Functions of copper braid
block noiseand crosstalk
provide achannel for return signal
Why a wire pair is not used to connet aerial to receiver?
wire pair hassmall bandwidth
there is noise and crosstalk
large signal attenuation
Section 6. Operational amplifier
Structure of a metal-wire strain gauge
plastic insulating casingthat contains the wire
winding grid shape of wireso that deformation of wire is significant under external pressure
Assumptions of ideal operational amplifier
infinite open-loop voltage gain
(voltage output) / (voltage input) = infinity
infite input resistance
so that there is no lost volts due to internal resistance
zero output resistance
so that there is no internal resistance
infinite slew rate
so that output signal changes simultaneously with input signal
infinite bandwidth
zero noise contribution
Negative feedback
Feedback: part of output signalis sent back andcombined with input signal
Negative: feedback signal alwaysmakes input singal smaller
Benefits of negative feedback
increase stability
increase bandwidth
less distortion of output
Why there is avirtual earth pointininverting amplifier?
gain of amplifier is large
V+ is earthed
amplifier is not satureddue to the negative feedback
so V- must be very close to V+so V- is considered as virtual Earth point
Why arelayis required?
the appliance circuit requires high power and high current
but the control circuit can only provide a small current
Section 7. Electromagnetism
1 Coulomb fields
Kinetic energy of charges determines the closest distance particles can get due to energy conservation (17 MJ 43 Q5)
Why is theelectric field strength zero inside conducting spheres?
chargesin a conductor willmoveif there is an electric field
charges will move until E=0
Whycharges on a spherecan beconsidered to act as a point charge at its centre?
electric field lines created by a sphere are radial and perpendicular to sphere's surface. These lines appear to come from the centre of sphere
Gravitational forces are not consideredwhen calculating force between charged particlesbecause gravitational force is about 30 orders of magnitudes smaller
2 Capacitor
Uses of capacitors in electrical circuits
smoothing ofrapid changing current
store electrical energy
block direct current
used in timing circuits
3 Magnetic fields
Why is thespeed of particle not affected by magnetic field?
frocefrom magnetic field on the particle isperpendicular to velocity
sono work is doneby the force on particle and speed will not change
Why thepath of electronin the magnetic field isarc of a circle?
when electron is moving perpendicular to magnetic field, the force from magnetic field on charge isalways perpendicular to its velocity
magnitdue of force is constant
so it act ascentripetal force
4 Velocity selector
Explain how velocity selector using auniform magnetic and electric fieldwork
uniformelectric field E and uniform magnetic field B are applied in the same region in space, and arenormal to each other
charged particles enter the region of fields withvelocity v perpendicular to both B and E
B exerts a force on charge due to F_B = Bqv
E exerts a force on charge due to F_E = Eq
B and E are setted so they exert forces inopposite directions(need to use fleming's left hand rule here)
F_B = -F_E for particles with a particular selected speed
these particles will move instraight linesacross region of field and leave the selector
particles withdifferent velocitywill bedeflectedand absorbed by the selector before leaving region of field
5 Hall effect
Hall voltageis developed across faces that areperpendicular to current and magnetic field
Describe the process how Hall voltage is setted up
magnetic field Bthat isperpendicular to the current Iis applied across the material
charge carriers in material will experience aforce that is perpendicular to both I and B
charge carriers will deflect and build-up so results in apotential difference V_Hacross the material
charge carriers stop building up and V_H becomes constant when F_B = F_E
V_H = BI/ntq
heret is the thickness of the side that is parallel to magnetic field
Why the Hall voltage isdifficult to detect in a thin slice of copperandeasier in semiconductor?
in copper (or any other metal)number density of electron is very large
so hall voltage will be very small
semiconductor has smaller values of n
Hall voltage can work on semiconductors withnegatively charge carriers(electrons) andpositively charged carriers(holes). What is difference of VH developed in the two different types?
using fleming's left hand rule, we can findmagnetic field will deflect holes and electrons in the same direction
butholes and electrons have opposite charge
so Hall voltage will haveopposite polarity
6 Eddy current
Whyeddy currentdissipates energyfrom moving conductor in uniform magnetic field?
as conductor moves into or out of the uniform magnetic field, it experienceschanging magnetic flux linkage
due to Faraday's law there will beeddy currents induced on the conductor
eddy currents produce heatingaccording to P=I^2*R
kinetic energy of moving conductorthus isconverted into thermal energy and electromagnetic energy
so moving block will slow down
7 Domestic use of AC
AC: current or voltage thatreverses polarityperiodically
period T, frequency f, peak voltage V0, voltage as a function of time
Why does heating occur when an AC is applied across a resistor while the average current is zero?
average current is zero because AC current hasnegative and positive currents that will cancel each other
heating power depends on I^2*R and I^2 isalways positive, so heating effect will not cancel out
Root-mean-square (rms) voltage: the DC voltage that produces the same power is a resistor as an AC voltage with peak value V0 isV0/sqrt(2)
Why rms current in an air-cored solenoid is reduced when an iron core is inserted?
inserted coreincreases rate of change of flux linkage
soinduced emf in solenoid is increased
the induced emf is in opposite direction to the applied emf so current will be reduced
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