ELECTRICITY AND MAGNETISM

ELECTRICITY AND MAGNETISM

1. D.C. circuits

   • Series and Parallel arrangements
     • 1. adding additional components in series reduces the e.m.f. between the original components.
     • Combine resistors
       • Resistors In Series
         • 1.[additional resistor increases the length of the path taken by charges. R↑] 2. R=∑Ri derived: ε=V=∑Vi.by K'2 law. IR=I(R1+R2+...Rn). Iin=Iout by K'1 law. R=R1+R2+...+Rn=∑Ri.
       • Resistors In Parallel
         • 1.adding branches,more current drawn from power supply. [aditionall resistor provides another path for the current, increasing the cross-sectional area, R↓] 2. I=∑Ii=I1+I2+...In.by K'1 law. V=I1R1=I2R2=I3R3... since p.d.=EMS in each loop of K'2 law. Therefore, I/V=I1/V1+I2/V2+...In/Vn. 1/R=1/R1+1/R2+...1/Rn.
     • Combine EMFs/ cells
   • Kirchoff's laws
     • 1st ∑I in=∑I out, junction
       •  in junction
       • conservation of charges: charge cannot be created or destroyed...
     • 2nd ∑ε=∑V, loop
       • In a closed loop,
       • conservation of electrical energy: energy cannot be destroyed or created...
       • [In each components, sum of potential drops is equal to sum of potential gains.]
   • Potential Divider
     • a series arrangement of resistors. changable Vout= share of power supply.
     • [shares] potential divider equation: Vin/Vout=(Rt)/Rout
     • loading: paralleling Rout with another resistor of high resistance
       • max power delievered of power supply when Rload=r
     • appli. electronic sensors
       • sensitivity: gradient in graph
       • heater made of themistor: R∝1/T
         • themistor used to moniter the change in temperature.
       • 感光灯 made of LDR: R∝1/Intensity
     • appli. potentiometers
       • a variable resistor with 3 terminal and sliding contact. to change Vout: sliding...length of resistor that current go through varies, resistance varies, Vout varies.

2. Current of Electricity

   • Resistance and Resistivity
     • Resistance R=△V/I
       • ratio of p.d. across a component to the current flowing it.
       • expri. plotting I-V graph
         • to plot I-V graph connecting one component with a variable resistor and parallelling voltmeter to that component: 1.connect circuit up... 2.vary resistance. 3.measure current (I) and p.d.(V), disconnect circuit between readings. 4.obtain a range of results. 5.reverse connections to power supply and repeat(第三象限的图). 6.plot a graph of I against V, gradient=(1/R). for semiconductor diode:  x-intercept 0.6V.
         • [notice] switch off circuit between readings to avoid energy wasted internally of the cell.
       • one ohm
         • resistance (of a resistor) of 1A current flowing through it at 1v p.d..
     • Resistivity ρ=RA/L
       • defined as the resistance of a material of unit cross-sectional area per unit length.
       • conductivity is the inverse of resistivity. both are properties of metal. (why resistivity is but resistance not: since ρ is independent of dimensions of specimen of material.??)
       • experi. determine ρ
         • 1.measure: length of wire(meter rule). diameter of wire(venirer caliper) voltage of...(voltmeter) amplitude of...(amper meter) 2.calculate: cross-sectional area(A=...=πd) resistance(R=V/I) 3.repeat experiment for different[L] 4.(ρ=R(A/L) R, A unchanged. L changable.) plot a graph of [R against L] gradient is[ρ/A], ρ=Axgradient.
         • notice: overheat/ wasted of battery: switch off between readings
   • Typical metallic conductors with I-V graphs
     • some obeys ohm's law, and some does not. [we focus on characteristics of them]
     • metallic/ ohmic conductor
       • constant resistance(ratio)  since it obeys ohm's law at constant T. -->initially in metal: protons are regularly localised and surrounded by delocalised e- .
     • filament lamp
       • I increases with V increases. R increases with T increases. since high T resulting in an increase in the amplitude of vibration of ions and the collision frequency of e with the lattice ions. 
     • themistor
       • made by semi-conductor. R decreases with T increases(when V increases). since more charge carriers from the lattice are released, reducing the resistance of the themistor.
     • semi-conductor diode
       • a diode allows current to flow in one direction only. and
     • LDR
       • made by semi-conductor. R decreases with In increases.R varies with the intensity if light falling on it.
   • Ohm's law I∝V
     • the current in a component is proportional to p.d. across it provided physical conditions(eg.Temp) stay constant.
   • EMF =ε =W/Q: energy transfered from non-electrical forms into electric form per charge
     • distinguish between EMF and p.d. in terms of energy consideration. eg. EMF--p.d.  chemical cell--bulb
     • ε=(terminal p.d.) + (lost volts): effect of internal resistance (r) of power source of EMF on termial p.d.
       • 1.internal resistance (r): the resistance of material of cell. 2.it resulted in lost volts: while current flows, more charges travel through cell each second, more work is done by the charges, increasing 'lost volts', lower terminal p.d.
       • experi. cell with variable resistor
         • V=(-r)I +ε  notice: 1)fixed value resistor: keep the current low,prevent short-circuit/over-heat of battery. (which lead increases in r). (2)r changes when T increases, always switch off between each measurements.
         • (chemical) cell: anode ++++ cathod ------
         • Q: how to connect variable resistor
       • appli. small r: prevent overheating OR wasted in energy; high r: safety feature
   • I=Q/t [A]
     • rate of flow of charge. conventional direction: +terminal to -terminal.
   • [charges passing a point] Q=It [C]
     • product of steady current and time interval for current passing a point.
     • one coulomb
       • charge flows in 1s of 1A current passing a point.
   • [transmitted power] P=VI=I^2R=V^2/R
     • [Et] kWh
       • energy transferred by a device working at 1kW for 1h.
   • p.d. in circuit: difference in voltages between two points in circuit
     • p.d. =△V = W/Q: energy transfered from electric form to other forms per charge across a component
       • Q:zero p.d./ reading in voltmeter: no current flow
       • one volt: △p.d. 1J->1C between points
         • is the p.d. between points when one joule energy is transferred by one coulomb current passing from one point to the other.
     • bold p.d.: △potentials in electric fields created by e-
       • it is defined as the difference in potentials of electric field created by electrons.(other than the current/flowing e- ->no current, p.d.exists)
   • Fuse: safety device stops current flowing of [1A, 13A]

3. Charge Carriers

   • delocalised e- as charge carriers in metal
     • 1.particles have charge. 2.(motion)delocalised electrons move through the wire, randomly colliding with the positive ions (for which are vibrating around fixed position) as they drift past them. 3.(model)lattice of positive ions surrounded by a number of delocalised e-.
     • Temperature effect: T↑, Amplitude of vibration of the lattice ions↑, conduction electrons slowing their process along the circuit hence R↓
     • in Semiconductor
       • current flows when p.d. applied. common unit mA
       • Temperature effect
         • 1. weekly bounded atoms' escaption, conduction electrons↑
         • 2. amplitude of lattice vibrations↑ leads to R↓
         • 3. current flow causes a heating effect, more conduction electrons I↑, R↑
         • 1>2, leads to R↑ as T↑
   • drift velocity Vd=X/t
     • average displacement travelled of e- along the wire per second.
     • mean drift velocity: v=I/nAq
       • v. drift velocity.(average). A. cross sectional area. q. charge on each charge carrier. n. number density.number of charges per volume.
   • charge on charge carriers are quantised: N=Q/Qi
     • experi. Millikan oil drop
   • delocalised ions as charge carriers in eletrolytes
     • (motion)free ions move through liquid. [notice: anode+, cathod-; cations(+ions), anions(-ions)]

4. EF

   • Field strength E=F/Q [NC-1]
     • the force experienced per unit positive charge. (is a vector quantity)
   • Radial fields
     • a region where a charge experiences a force.
     • Coulomb's law F∝Qq/(r^2)
       • force between two charges is proportional to their charges and inversely proportional to the quare of their seperation.
       • F= 1/(4πε) · Qq/(r^2)
         • permitivity of free space ε
     • Field lines: arrows-direction, spacing-strength
     • E=1/(4πε) · Q/(r^2)
   • Uniform fields
     • E=V/d [Vm-1]
   • Potential: PE C +Q
     • is potential energy that each columb of positive charge would have if placed at that point.
     • p.d.: △V=W/Q

5. Capacitors

   • C=εA/d
     • ε=(εo)(εr)
       • εo: permitivity of free space εr: relative permitivity

6. ELECTROMAGNETIC INDUCTION

   • is the production of e.m.f. (electromotive force, or voltage) across an Electrical Conductor in a Changing Magnetic Field.
   • Q: 壹 e.m.f. OR voltage all can be state? 贰 Electrical Conductor: ①single Conducting (Aluminium) ring. ②Coil. ③等等 叁 how does M-F change. → strength OR flux dnesity changes. B = (μ/ 2π)(I / r). → using AC current OR induce relative motion (between magnet and coil) can change M-F (periodically).
   • Faraday's Law: e.m.f = -△NΦ/ △t = - △N(BA)/ △t
     • 壹. the minus sign comes as a nature of induced e.m.f from Lenz's law. 贰. hence we could vary e.m.f. by B, N, A, t.
   • Lenz's Law: (D induced current/ e.m.f.) oppose (D △Φ)
     • (fact) direction of induced e.m.f. is always opposite to the direction of change of magnetic flux.
     • (derivation) conservation of energy.  KE → EPE. to understand when current is induced, another B-F is created by the current, if flux increases in the same direction with the previous flux, energy is increased other than conserved. therefore increased flux have to be in opposite direction with the previous, and induced current have to be opposite to the increment of flux.
   • Q: how does e.m.f. be induced in specific case
     • some Q about specific reason for e.m.f. is induced,  壹. e.m.f is induced as changing in magnetic flux due to the variable nature of AC current.  贰. (Faraday's model) e.m.f . is induced by relative motion between magnets and coil.(changing r of B=()(I/ r)).
   • Q: how does current be induced in specific case
     • *  壹. current only flows in a complete circuit and be drove by (induced e.m.f.). 贰. from Lenz's law, Direction of induced current is opposite to the Direction of increment of magnetic flux??. 叁. furthermore, current can induce a M-F ??
     • juice: 2 models supported by RelativeMotion + M-F → Current
   • Force experienced??
     • a current- carrying conductor in M-F will consequently experience a force?
   • application
     • [alternating current/ e.m.f.] AC Generator
       • a device produces e.m.f. by changing Number of magnetic flux (variable flux linkage), passing through a wire coil.
     • Transformer
       • changable primary B-F due to alternating e.m.f. Varying flux linkages with the secondary coil.? e.m.f. is induced in second coil as there is a rate of change of flux linkages.
       • ①: Step-up. Ns < Np, so more voltage on primary coil. ②: Step-down. Ns > Np, so less.
       • energy loss
         • ① Flux leakage
         • ② Hysterysis losses
         • ③ Iron losses (Eddy current)
         • ④ Copper losses
         • → Eddy current arises

7. B-F: region ar Magnet, MC. MF is experienced.

   • is a region around a Magnet OR Moving Charges in which a Magnetic force is experienced.
   • (introduction to Field) 壹. Field: a region around a Mass, Moving Charge or Magnet,... in which a force can be experienced. 贰. → 具象化. lines of flux/ force 具象化 B-F.
   • F=(B)(I)(sinθ)(L) in straight wire = (B)(v)(sinθ)(Q) in solenoid
     • 壹. 壹 θ: angle between flux lines (D of B-F) and conventional current. 壹. 贰. L: length of straight wire. 贰. 壹.v: speed of positive charge. 贰.贰. θ: angle between moving direction of speed v and B-F.
     • appli. ① charge deflects in B-F: F = BQv = centripetal Force. ② be in equilibrium in B-F & E-F: F = Bqv = qE.
   • 具象化 → Lines of Flux: Direction & Strength
     • or so-called lines of force: 壹. arrow shows the direction of force/ field. 贰. spacing/ seperation between lines shows strength of fields/ how strong the field is.
     • property: always perpendicular to the surface. and never cross each other.
     • lines/ Flux Density → Strength: B = (μo/ 2π)(I/ r) in straight wire = (μo)(n)(I) in solenoid [T]
       • 壹. μo: permeability of free space / is the measure of effect of material itself on B-F. 贰. I: conventional current. 叁. r: distance from centre of wire. 肆. N: # of turns per meters.
       • 1T comes from B = F/ (ILsinθ). IT= 1 N/ (Am): 1T is at which a wire of 1m length and 1A current perpendicular to the field experience a force of 1N
       • [detector] Hall probe → Vh = BI/ (nte) = BI/ (Aned)
         • is a B-F / B sensor passes current when the sensor is placed perpendicular to B-F.
         • Hall Voltage derivation:
       • Flux Φ = (B)(A)(cosθ) [Wb]
         • A: cutting cross-sectional area. Φ: BA = relative movement in B-F (increases from initial zero Φ).
         • Flux Linkage (N)(Φ) = (N)(B)(A) [Wb-turns]
           • in words. it is the product of flux and number of turns.
       • {B ∝ μo}
         • appli. put ferromagnetic core inside solenoid
           • atomic magnets of core line up along the lines of flux inside solenoid, core becomes magnetised. increases μo.
           • solenoid is made of turns of coils.
   • Direction of B, F, I
     • [right-hand grip rule] B & I
       • 1.use direction of straight wire current (thumb direction) to perdict D of magnetic field (grip direction). 2.use D of MF (grip direction) to perdict D of I (thumb direction).
       • 1.clockwise, anticlockwise. 2.not + but N pole/out, S pole/into
     • [Fleming's left-hand rule] F ⊥ B ⊥ I
       • F: force [thumb] B: field [first finger] I: current [second finger]
     • N → S
     • S: clockwise B-F, N: anticlockwise B-F
   • common models
     • 1. single coil. 2. bar magnet. 3. single straight wire. 4. solenoid (turns of coils). 
   • experiment
     • device: ① Galvanometer
       • Galvanometer: is a type of Ammeter, and used for small electric current.

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