2 Electricity Consider a force like gravity but a billion-billion-billion-billion times strongerwith two kinds of active matter:electrons and protonsand one kind of neutral matter: neutronsTwo important laws:Conservation & quantization of chargefrom experiment:Like charges repel, unlike charges attract
4 Electric Properties of Matter (I) Materials which conduct electricity well are called___________Materials which prohibited the flow of electricity are called _____________‘Earth’ or ‘ground’ is a conductor with an infinite reservoir of charge_____________ are in between and can be conveniently ‘switched’_____________ are ideal conductors without losses
6 Coulomb’s Law Force on a charge by other charges ~ ~ Significant constants:e = (63) 10-19C i.e. even nC extremely good statistics(SI) 1/4pe0
7 Find F1 Principle of superposition of forces: If more than one charge exerts a force on a target charge,how do the forces combine?Find F1Luckily, they add as vector sums!Consider charges q1, q2, and Q:F1 on Q acc. to Coulomb’s law0.29NComponent F1x of F1 in x:With cos a = > F1x=Similarly F1y =What changes when F2(Q) isdetermined?What changes when q1is negative?
8 Electric FieldsHow does the force ‘migrate’ to be felt by the other charge?: Concept of fields
10 Charges –q and 4q are placed as shown. Of the five positions indicated at1-far left, 2 – ¼ distance, 3 – middle, 4 – ¾ distanceand 5 – same distance off to the right,the position at which E is zero is: 1, 2, 3, 4, 5
11 Electric field linesFor the visualization of electric fields, the concept of fieldlines is used.
12 Electric Dipoles Net force on dipole by uniform E is zero. Product of charge and separation ”dipole moment” q dTorque
30 Moving charges: Electric Current Path of moving charges: circuitTransporting energyCurrentRandom walk does not mean ‘no progression’Random motion fast: 106m/sDrift speed slow: m/se- typically moves only few cmPositive current direction:= direction flow + charge
31 Work done by E on moving charges heat (average vibrational energy increased i.e. temperature)Current through A:= dQ/dtcharge through A per unit timeUnit [A] ‘Ampere’[A] = [C/s]Current and current density donot depend on sign of charge Replace q by /q/Concentration of charges n [m-3] , all move with vd, in dt moves vddt,volume Avddt, number of particles in volume n AvddtWhat is charge that flows out of volume?
32 Resistivity and Resistance Properties of material matter too:For metals, at T = const. J= nqvd ~ EProportionality constant r is resistivity r = E/J Ohm’s lawReciprocal of r is conductivityUnit r: [Wm] ‘Ohm’ = [(V/m) / (A/m2)] = [Vm/A]
34 Resistance Ask for total current in and potential at ends of conductor:Relate value of current toPotential difference between ends.For uniform J,E‘resistance’ R = V/I [W]vs. RR =rL/AR = V/IV = R II = V/R
36 Group TaskE, V, R of a wireTypical wire: copper, rCu = 1.72 x 10-8 Wmcross sectional area of 1mm diameter wireis 8.2x10-7 m-2current a) 1A b) 1kAfor points a) 1mm b) 1m c) 100m apartE = rJ = rI/A = V/m (a) 21 V/m (b)V = EL = 21 mV (a), 21 mV (b), 2.1 V (c)R = V/I = 2.1V/1A = 2.1 W
37 Electromotive ForceSteady currents require circuits: closed loops of conducting materialotherwise current dies down after short timeCharges which do a full loopmust have unchanged potentialenergyResistance always reduces UA part of circuit is needed whichincreases U againThis is done by the emf.Note that it is NOT a force buta potential!First, we consider ideal sources (emf) : Vab = E = IR
38 I is not used up while flowing from + to – I is the same everywhere in the circuitEmf can be battery (chemical), photovoltaic (sun energy/chemical),from other circuit (electrical), every unit which can create em energyEMF sources usually possess Internal Resistance. Then,Vab = E – Ir and I = E/(R+r)
39 Circuit DiagramsVoltage is always measured in parallel, amps in series
40 Energy and Power in Circuits Rate of conversion to electric energy: EI, rate of dissipation I2r –difference = power output sourceWhen 2 sources are connected to simple loop:Larger emf delivers to smaller emf
41 Resistor networksCareful: opposite to capacitor series/parallel rules!
45 Kirchhoff’s Rules A more general approach to analyze resistor networks Is to look at them as loops and junctions:This method works evenwhen our rules to reducea circuit to its Reqfails.
46 ‘Charging a battery’Circuit with morethan one loop!Apply both rules.Junction rule,point a:Similarly point b:Loop rule: 3 loopsto choose from‘
47 Group task: Find values of I1,I2,and I3! 5 currentsUse junction ruleat a, b and c3 unknown currentsNeed 3 eqnLoop rule to 3 loops:cad-sourcecbd-sourcecab(3 bec.of no.unknowns)Let’s set R1=R3=R4=1Wand R2=R5=2W
48 Capacitance E ~ /Q/ Vab ~ /Q/ Double Q: Charge density, E, Vab double tooBut ratio Q/Vab is constantCapacitance is measure of ability of a capacitor to store energy!(because higher C = higher Q per Vab = higher energyValue of C depends on geometry (distance plates, size plates, and materialproperty of plate material)
49 Plate Capacitors E = s/e0 = Q/Ae0 For uniform field E and given plate distance dVab = E d= 1/e0 (Qd)/AUnits: [F] = [C2/Nm] = [C2/J] … typically micro or nano Farad
50 Capacitor NetworksIn a series connection, the magnitude of charge on all plates is the same. The potential differences are not the same.In a parallel connection, the potential difference for all individual capacitors is the same. The charges are not the same.
51 Equivalent capacitance is used to simplify networks. Group task: What is the equivalent capacitanceof the circuit below?Step 1:Find equivalent for C series at rightHand.Step 2:Find equivalent for C parallelleft to right.Step 3:Find equivalent for series.
52 Capacitor Networks 24.63 C1 = 6.9 mF, C2= 4.6mF Reducing the furthest right leg(branch):C=Combines parallel with nearest C2:C =Leaving a situation identical to what we have just worked out:Charge on C1 and C2:QC1 =QC2 =
54 Energy Storage in Capacitors 24.24: plate C 920 pF, charge on each plate 2.55 mCV between plates:V = Q/C =b)For constant charge, if d is doubled, what will V be?If q is constant,c) How much work to double d?U =If d is doubled, C Work equals amount of extra energy needed which is
55 Other common geometries Spherical capacitorNeed Vab for C, need E for Vab:Take Gaussian surface as sphereand find enclosed chargeNote:Cylindrical capacitorFind E Er = l/2pe0 1/rFind V Vab =Find C Q =What is C dep. On?
56 Dielectrics Dielectric constant K K= C/C0 For constant charge: Q=C0V0=CVAnd V = V0/KDielectrics are neverperfect insulators: materialleaks
57 Induced charge: Polarization If V changes with K, E must decrease too: E = E0/KThis can be visually understood considering that materialsare made up of atoms and molecules:
59 Change with dielectric: E0 = s/e0 E = (s-si)/e0 and = E0/K s-si = e0E0/K si = s -s/Ksi = s (1-1/K)E = s/eEmpty space: K=1, e=e0
60 RC Circuits From now on instantaneous Quantities I and V in small fontsvab = i Rvbc = q/CKirchhoff:As q increasestowards Qf,i decreases 0Charging a capacitorSeparate variables:Integrate, take exp.:
61 Discharging a capacitor Characteristic time constant t = RC !Discharging a capacitor
62 charged fully after 1[hr]? Y/N Ex C= 455 [pF] charged with 65.5 [nC] per plateC then connected to ‘V’ with R= 1.28 [MW]iinitial?b) What is the time constant of RC?i = q/(RC) =[C/(WF] =! [A]b) t = RC =Group Task:Find tcharged fully after 1[hr]? Y/N
63 Ex 26.82 C= 2.36 [mF] uncharged, then connected in series to R= 4.26 [W] and E=120 [V], r=0Rate at which energy is dissipated at Rb) Rate at which energy is stored in C increasesc) Power output sourcea) PR =b) PC= dU/dt =c) Pt = E I =d) What is the answer to the questions after ‘a long time’? all zeroGroup Task