4C. Electrochemistry and Electrical Circuits and their Elements

Describe electrical potential and potential energy Equation Distance Change in potential Work done? Electron volt Concept of W

*Charged* particles make a vector field (electric field) but also a *scalar field (electric potential)* Electric potential: *Φ = k (Q/r)* >> as r increases, potential decreases Units = J/C = *volt (V)* *Potential is same* at every point at same distance, since *no direction* - *equipotentials* Change in electric potential energy: *ΔPE = qΔΦ=qV* - Voltage is the change in electrical potential *Positive* particle will gravitate towards *lower* potentials *Negative* particle will gravitate towards *higher* potentials Work done in an electric field: *W(by grav) = -ΔPE(grav)* Electron volt (eV): - An electron moving through with a potential difference of 1V experiences a kinetic energy change of *1.6e-19J = 1eV* ~~~~~~~~~~~~ For *vector* quantities (force, acceleration) F = qE a = F/m = qE/m For *scalar* quantities (speed, energy, work) Ultimately, moving *with* nature *decreases* potential energy (moving *against* nature *increases* potential energy) - *W*(by grav) = *-ΔPE*(grav) - *W*(against grav) = *+ΔPE*(grav)

Diameter of wire is 2mm (cross-sectional area of 3.3e-6). What would be the resistance of a 800m wire? Resistivity = 1.7e-8Ω

*R = δ x (L/A)* = *4Ω*

Describe conductors, insulators, and polarization

*[Conductors]:* contain charges that are free to roam throughout the material - e.g. metals In metals one or more valence electrons can move. In an electric filed the electrons respond to the field and are known as *conduction electrons* Can use metal to *shield* an object, as metal's electrons will go to the *surface*, shielding the interior so that *E=0* *[Insulators]:* does not have free charges, with electrons *tightly bound* to atoms. *[Effects of adding a charge]:* i. *Neutral conductor* - Adding Q+ causes a *separation of charge* and thus a *net* force ii. *Neutral insulator* - Adding Q+ causes *polarization* and a slight net force - Not as dramatic but still a force

Describe electric charge Describe electric force and coulomb's law Describe the principle of superposition for electrical forces

*[Electric charge]:* *Elementary charge* - *e+* = positive - *e-* = negative - *coulombs* (C) is the unit; *e = 1.6e-19 C* e.g. Flouride = -1e (or -1.6e-19C) e.g. Calcium = +2e (or 3.2e-19C) 1nC = 1e-9C *Total* electric charge is always *conserved* *[Electric force]:* *Electric force* (F(e) exists between *two* charged particles: Coulumn's Law *F(e) =k [ (|q1 q2|) / r²* >> where r is the distance between the particles >> where k is the proportionality constant (depends on material between particles >> should use *ko = 9e9* (for empty space / air) *[Principle of superposition]:* A principle that allows us to *sum* the *individual electric forces* acting upon an atom Allow us to calculate the *net electric force* ~~~~ 1C charge = 9e9 N of force (damn)

Describe electrochemistry: Electrolytic cell Electrolysis Anode, cathode Electrolyte Faraday's Law Electron flow; oxidation, and reduction at the electrodes

*[Electrolytic cells]:* i. *[Electrolysis]:* - Requires *external* potential/voltage input (e.g. a battery) (*negative* cell voltage - Battery *forces* electrons to flow (forces *nonspontaneous* redox rxn to occur) - Useful for *electroplating* ii. *Anode, cathode* - *Anode* is where *oxidation* occurs - *Cathose* is where *reduction* occurs, sticking to a plate iii. *Electrolyte* - *Ions* = electrolyte - *Conduct* electricity by the *motion* of ions iv. *Faraday's Law* - Law of electrolysis: Amount of *chemical change* is *proportional* to amount of *electricity* that flows through the cell v. *Electron flow at electrodes* - *Anode = oxidation* = loss of electrons from substance - electrons move to cathode - *Cathode = reduction* = electrons jump into substance

Galvanic or Voltaic cells - Half-reactions - Reduction potentials; cell potential - Direction of electron flow Concentration cell Batteries - Electromotive force, - Voltage Lead-storage batteries - Nickel-cadmium batteries

*[Galvanic/Voltaic cells]:* - *Spontaneous* electron flow (*Positive* cell voltage) - Anode *degrades* from ox, cathode *accumulates* from red - *Salt bridge* binds to *remainder* ions, (they are inert, i.e. *spectator ions*)i. - *Standard conditions* = *1atm , 1M, 25oC* - Potentials are made where one half cell is the substance of interest and the other is *Hydrogen*, since a full 1/2-1/2 hydrogen cell potential = *0V* i. *Half-reactions* - Oxidation = *loss* of e- = - Reducation = *gain* of e- = ii. *Reduction potentials; cell potential* - *Cell potential* (whether spontaneous(+) or not (-)) = *Potential(Red)+ Potential(Ox)* - *Reduction potential* = potential of the reduction *half reaction* >> Where *oxidation potential* is just the *reverse sign* ii. *Direction of electron flow* - *Anode --> Cathode* - *More positive* reduction potential = *stronger oxidizing* agent, *weaker reducing* agent - *More negative* reduction potential = *stronger reducing* agent, *weaker oxidizing* agent *[Concentration cell]:* - *Identical electrodes* but different half-cell concentrations - Potential difference is not from difference in electric potentials, but rather the differing concentrations - Electrons move down *concentration gradient* until concentrations are the *same* *[Batteries]:* - Rechargable batteries i. *electromotive force* - *discharge* (via *galvanic*) and *recharge* (via *electrolytic*) ii. *lead-storage* (1) Pb+HSO4- --> PbSO4 + H+ + 2e- (2) PbO2 + HSO4- + 3H+ + 2e- --> PbSO4 + 2H2O iii. *nickel-cadium* (1) Cd + 2OH- --> Cd(OH)2 + 2e- (2) 2NiO(OH) + 2H2O + 2e- --> 2Ni(OH)2 + 2 OH-

Describe Ohm's Law What materials Resistors Process of analyzing circuits - series - parallel

*[Ohm's Law]:* - (just a reaarrangement) *V = IR* - A material is "ohmic" if its resistance is *constant* at voltage *varies* - Also if current reverses direction if polarity of voltage is swapped *[Resistors]:* - A component of a circuit with a *known resistance* - Usually an *alloy* of carbon,nickel and copper) *[Analyzing circuits]:* - Firs stop is transforming resistors into a simple singular one (*equivalent resistor*)to understand *overall* circuit resistance Resisters in *series* if each *follows* each other along a single connection path - *R(sum) = R1 + R2* - Sum is larger than biggest resistor Resistors in *parallel* if each provides an *alternate route* from one circuit to another - Sum is smaller than smallest resistor - For *two* parallel resistors >>*R(sum) = R1R2 / R1 + R2* - For *>2* parallel resistors >> *1 / R(sum) = 1/R1 - 1/R2*

a. Find the current of the following circuit (Press i) b. Find currents and voltages through the individual resistors

*[a.]* Series = 8Ω + P1 P1 = (5x20)/(5+20) = 4Ω Total = 12Ω I = V/R = 60V / 12Ω = *5A* *[b.]* Start *bottom*, then *up*, then *left* If go back to *series* combo --> bring *I* If go back to *parallel* combo --> bring *V* 1. I = 5A - from overall circuit in part (a) 2. Go back to *series* combo - bring back *current* >> recall that we converted parallel to into a single 4Ω in (a) - V=IR - R1 = (5A)(8Ω) = 40V - R2 = (5A) (4Ω) = 20V 3. a. Go back to *parallel* - bring back *voltage* = 20V b. For R1, give it its regular 40V - since resistor doesnt change going back to this c. Find current of parallel components - top: i = (20V x 5Ω) = 4A - bottom: (20V x 20Ω) = 1A Final answer R1 has 40V, with 8Ω and 5A P1(top) has 20V, with 5Ω and 4A P1(bottom) has 20V, with 20Ω and 1A

Describe capacitors Properties Charges - equation Capacitance Electric fields Storage

- A pair of conductors with *equal opposite* charges - Often as metal plates called "*parallel-plate capacitors*" - Often look like *||* or *|(* - Used to *create* electric *fields* - Used to *store* potential *energy* Plate connected to *positive* terminal becomes *positively* charged Plate connected to *negative* terminal becomes *negatively* charged Potential *difference* of plate opposes potential difference of battery - Charge *stop* flowing once plate *matches* battery Charge of capacitor *(Q) = CV* >> C is constant (capacitance) >> V is potential difference between capacitor plates >> unit is C/V (*farad*) *Capacitance = eo x (A/d)* - eo = constant (permitivity of free space) = 8.85e-12 - A = area of each plate - d = separation - A measure of plates' capacity to hold a charge (holds change per volt) *[Capacitor electric fields]:* - Ed's formula: *V = Ed* >> determines *strength* of field - Field is *uniform* *[Storage of potential energy]:* - Charging a capacitor transfers electrons from one plate to the other. After transfer the empty plate is (+) and saturated plate is (-). - Charging is increasing more difficult to do as harder to remove electrons from increasingly (+) and add to increasingly (-). - Thus requires work to transfer more charge, which is stored as potential energy Electrical PE stored in a capacitor: *PE = (1/2) Q V* >> can rearrange considering Q=CV *Discharge* is when u let the potential energy go back *down* its *gradient* - Tap into the energy stored to do *work* >> gradient decreases exponentially as overall energy declines

1. How much positive charge is contained in 1 mole of carbon atoms? negative charge? total charge? 2. Two charges, q1 = -2e-6 C and q2 = +5e-6C, are separated by a distance of 10cm. Describe the electrical force between these particles 3. Press i, q1 = 2C, q2 = -8C, q3 = -1nC. If r=1, and R=2m, which one of the following vectors best illustrates with direction of the net electric force on q3?

1. 6 protons (q+ = +6e) Q+ = Na x (6e+) Q+ = Na x (6)(1.6e-19C) *Q+ = 6e5 C* *Q- = -6e5C* Total charge = Q+ + Q- = *0* 2. F(e) = k [ (-q1 q2) / r² F(e) = *9N* Thus feel 9N towards each other 3. F(on-3) = F(1-on-3) + F(2-on-3) F(1-on-3) = k [ (-q1 q3) / r² = *18N* away F(2-on-3)= k [ (-q2 q3) / R² = *18N* towards Which makes it go *Down right*

1. An electric dipole consists of two charges, +Q and -Q, where Q = 4uC, separated by a distance of d=20cm Find the electric field at the point midway between the charges 2. A positive charge, +q, is placed at the point labeled P in the field of the dipole shown (Press i). Describe the resulting electric force on the charge. Also for -q on point N.

1. E = ko (Q / (0.5d)²) >> rewrote r as 1/2d since midway E+ repels point towards Q- E- attacks point towards Q+ E = E+ + E- = *7.2e6* Ultimately moving *towards Q-* 2. Electric field vector is always *tangent* to the field line pass through that point, with a *direction same* to the field line *Pvector* goes at a tangent towards *Q-* *Nvector* goes at a tangent towards *Q+*

1. Let Q = +4nC be a charge that is fixed in position at the origin of an x-y coordinate system. What is the magnitude and directiono f the elecric field at the point (10cm, 0)? At the point (-20cm, 0)? 2. The magnitude of the electric field at a distance r from source charge is +Q = E. What will be the magnitude of the electric field at a distance 4r from a source charge +2Q? 3. A particle with a charge q=2 uC is placed at a point where the electric field has magnitude 4e4N/C. What will be the strength of the electric force on the particle?

1. Electric field at point A: - E = k(|Q| / r²) - E = 9e9 (4e-9 / 10²) = *3600* Since Q is positive, point A vector points away (in the *positive* x-direction) = *i* Electric field at point B: - E = *900* - points away in *negative* x-direction (since x-coordinate is left of charge) = *-i* 2. E = kQ/r² =*1/8*E 3. F=qE F = (2e-6 C)(4e-4) = *8e-2 N*

1. In the figure below, a particle whose charge is q+4nC moves in the electric field created by -Q Find, a. The change in potential energy b. The work done by the electric field c. The change in kinetic energy as moves A-->B d. If particle mass = 1e-8 kg and started at rest from A. what will be its speed as it passes through point B 2. An electric field pushes a proton from one position to another such that potential change = -500V. By how much does the kinetic energy of the proton increase, in eV

1. a. ΔPE = qΔΦ = *-2e6 J* b. W(byfield) = -ΔPE(elec) = *2e-6J* c. ΔKE = ΔPE(elec) = *+2e-6J* d. PE(at B) = ΔKE = +2 e-6 J - (1/2)mvB² = *20m/s* 2. ΔPE = qΔΦ = -500 eV ΔKE = -ΔPE = *+500eV*

1. A particle with a positive charge q and mass ms moving with speed v undergoes a uniform circular motion in a constant magnetic field B. If the radius of the particle's path is r, what expression gives the particle's orbit period? 2. A particle with a negative charge -q moving with a speed vo enters a region containing a uniform magnetic field B. If the vo makes an angle of 30o with B, what is the particles speed 8 seconds after entering the field? 3. A particle with charge q moves with velocity v through a region of space contianing a uniform electric field E, and a uniform magnetic field B. What is an expression for the total elecromagnetic force on the particle?

1. qvB = mv² / r r = mv / eB >> setting Fb=Fc e becomes q since proton Total distance = circumference = 2πr >> sub r in = *2πm / qB* 2. Magnetic forces do no work, speed is *unchanged* 3. F(e) = qE F(b) = q(vxB) total = F(e) + F(b) = *q(E + v x b)*

1. An area, A, of each plate of a parallel-plate capacitor satisfies eoA = 10e-10. If the plates are separated by a distance of 2mm and this space is filled by a sheet of mica with a dialectric constant of K=6. What is the capacitance? 2. The inner and outer surface of a cell membrane acts as plates in a parallel-plate capacitor. Consider a 1um section of an axon. The dialectric constant is 8 and the membrane is 6nm thick. If the voltage across the membrane is 70mV, what is the appoximate magnitude of charge that resides on each side of this 1um section? (Eo = 8.85e-12) 3. The capacitance of a certain capacitor whose plates are separated by a distance of 1mm is 4 pF. If the plates are moved apart to a distance of 2.2mm to accommodate a slab of porcelain of thickness 2.2mm that is then inserted between them, the capicatance becomes 12pF. What is the dialectric constant of porcelain?

1. C = K eo (A/d) = *3e-7F* 2. Q = CV = K eo (A/d) V Q = *1e-15C* 3. Ratio of: C(dial) / C(nodial) = K/2.2 Increased by factor 3 K/2.2 = 3 *K = 6.6*

Use the right-hand rule for 1-4

1. Fb = (*x*) if q is + = (*o*) if q is - 2. Fb = *↓* if q is + = *^* if q is - 3. Fb = *^* if q is + = *↓* if q is - 4. Fb = *<-* if q is + = *->* if q is -

1. A capacitor has a capacitance of 2nF. How much charge can it hold at a voltage of 150V. 2. A charged capacitor has a charge Q, and voltage between plates is V. What happens to C if Q is doubled 3. What will happen to capacitance of a parallel-plate capacitor if the plates were moved closer together, halving the distance between them? 4. How big would the plates of a parallel-plate capacitor need to be in order to make capacitance equal to 1F, if d=8.85mm? 5. The charge on a parallel plate capacitor is 4e-6C. If the distance between the plates is 2mm, and the capacitance if uF, whats the strength of the electric field between the plates?

1. Q=CV = *3e-7C* 2. Nothing, C is constant for a given capacitor (Q is proportional to V) 3. C = eo x A/d - C is inversely proportional to d - C *increases* by *factor 2* 4. C = eo x A/d Rearrange for A =*10e9* 5. Q=CV rearrange for V V=Ed rearrange for E E = *2000 v/m*

Describe the principle of superposition for electrical potential 1. Q1 = +10nC, Q2 = -5nC. What is the potential at point A? point B? 2. A charge q=1nC is moved from position A to position B, along with a path labeled a in the figure below. Find the work done by the electric field. How would your answer change iq had been moved from position A to position B, along the path 'b'? 3. An electric dipole consists of a pair of equal but opposite charges, +Q and -Q, separated by distance d. What is the elctric potential at the point (P) that's midway between the source charges?

1When multiple source charges, can just *add numbers* 1. Φa1 = ko (Q1 / rA1) = 3000V Φa2 = ko (Q2 / rA2) = -900V Φa = Φa1 + Φa2 = *2100V* ΦB = ΦB1 + ΦB2 = *300V* 2. ΔΦA->B = 300V - 2100V = -1800V ΔPE = qΔΦ = *- 1.8e-6J* 3. Potential is *zero* Electric field is not zero

Three uncharged capacitors are arranged in a circuit as shown After the switch (S) has been closed for a long time and electrostatic equilibrium is reached how much charge is on the 6 uF capacitor?

3uF and 6uF are in serices so = (3x6)/(3+6)=2uF 2uF is in parallel with 12uF; and thus both have same 12V voltage since connected to the terminals fo the 12V battery Q=CV = *24uC*

For a solution of H2CrO4, How much Cr would be plated after 48,250C of electricity is forced through cell?

48,250C = 1/2 Faraday = 1/2 mole of electrons Cr oxidation state is +6, so its half reaction would be Cr6+ + 6e- --> Cr (1 mole) >> For every 6 moles of electrons, make 1 mole Cr But dont have 6 moles have 1/2 moles, so (1/6) (1/2) = *(1/12)*

Describe electric circuits What is current circuits w/ and w/o currrent - direction? Equations Voltage Resistance - intrinsic

A pathway for the movement of electric charge *[Current]:* - *Net* movement of charge i. *Current present* - slight drift in a particular direction (*drift velocity*) - *average position* changes ii. *No current* - *Conduction electrons* in metals are always moving, but *no net* movement (average position of electrons do not change) >> no drift velocity (rate of crossing is equal both ways) Current (i) = *Q /t* - charge over time - units are coulombs per second (*C/s*) (*amp*ere) *[Voltage]:* - Creates a *current* - It is the *difference in potential* that cause conduction electrons to move in a certain direction - Recall negative particles (like electrons) move towards higher potentials *[Resistance]:* - *R = V / I* >> where V = voltage applied to the ends of an object - I = current - So (at constant voltage) R and I are inversely proportional - units = V/A = *Ω* i. *Intrinsic resistance* (resistivity)(δ) - Unique to each *material* >> L = length >> A = cross-section - *R = δ x (L/A)* A long thin wire and a short thick wire would have different resistances but same resistivity (since same material)

What is the equivalent or total resistance of the following resistors?

A series of resistors comprised of parallel + single + parallel so P1 + 1Ω + P2 = 5 + 1 + 24 = *30Ω*

Describe dialectrics Equation Induced energy Potential energy change - w/ battery on - w/ battery off

A slab of insulating material in between the plates Need to prevent capacitors from touching or else will *instantaneously discharge* without doing work Also *increases capacitance* - by a "dialectric constant *K*" >> in vacuum/air = 1 C(with dial) = K x C(nodial) = *K eo (A/d)* *Induced energy* - The *surface* of the dialectric becomes slightly *polarized* by the plates, creating its own *field* - *Net* field is E - E(induced) >> this is why dielectrics *weaken E* *Potential energy when adding dialectric* i. *Battery disconnected* Q remains *constant* , K *decreases* V since it *increases* C by factor of K >> *PE decreases* by factor K >> some goes kinetic >> some goes into dipole >> some heat production ii. *Battery connected* - Voltage between plates must match battery voltage, so battery gives additional charge to match - V remains *constant*, (and neither will E (Eds law)), K *increases* C, and thus Q *increases* too >> *PE increases* by factor K

When a magnet is placed in a magnetic field, it tends to align with the field, so that the vector from the S pole to the N pole of the magnet is parallel to the field lines Given a uniform magnetic field, B, in the figure, exerts the same magnitude of force on the N pole as S pole, and the magnetic force is along the field line, what can you say about the net force and the net torque on the magnet?

B exerts F(b) on N pole and -F(b) on S pole Net force is *0* - F(b) + -F(b) Net torque is clockwise to allign along field line

Describe magnets North vs south Alligning

Bar magnets create magnetic fields resembling magnetic field produced by a circular loop of a current-carrying wire *Eminating* field lines = *North* pole *Re-enter* field lines = *South* pole Poles always exist in pairs Can place a *metal* in an external magnetic field, causing *allignment* of the metal's dipoles (*magnetizing*) so it produces its own magnetic field

Describe electric fields Properties Directions Distance Field lines

Charges *alter* the *space* around them, creating electric fields in their vicinity. It takes *two* charges to create a *force*, but only one to create a field The *force* is applied by the *field* , not direction by the charge itself, which can *exert upon* another charge Electric fields are *vector fields*, where each point in space has a specific vector - *length* of vector tell the *strength* of the field at that point - *direction* of vector tells the direction of field that a *POSITIVE* charge would feel >>> x-acis (+) = *i*; (-) = *-i* >>> y-axis (+) *-j*; (-) = *-j* >> thus electric field vectors point *away* from *positive source charges* and *toward* negative ones. Electric field equation is just columbs law without the other q. But r is distance from source charge to vector: *E(by Q) = k(|Q| / r²)* *Distance* from source and vector is the main factor for *field strength,* where *farther* = weaker (*shorter* length) vector *magnitude* - so a circle around source all have same magnitudes to each other. *[Field lines]:* - Draw lines through vectors - Use *density* to determine strength of field >> *Close* field likes = *stronger* field >> *Spread* field lines = *weaker* field *F(on-q) = qE* >> F is force >> q is charge this feels the field >> E takes into account the field >>> E = k(|Q| / r²) ~~~~~~ At the same distance from Q, *magnitudes* should be the same but each *direction* is different - Thus the overall *field differs at each point*

Describe magnetic fields and forces Created by Forces? Equation? Magnitude? Right hand rule

Created by *moving* electric charges Within a magnet bar there are orbiting electrons creating microscopic currents Only *exerts* force on *moving* charges *Magnetic force* (B) = *q(v x B)* - v = velocity of charge - q = charge *Magnitude of magnetic force* = Fb = *|q|vBsinθ* >> unit is *tesla* (T) >> θ angle between b and v >> always *perpendicular plane* to *v* and *B* >>> can never do *work* and thus do not effect *kinetic energy*, only *direction* Magnitude depends on *direction*, which depends on *charge* of q: - *Parallel* to magnetic field = *0* force - *Perpendicular* = sin90 = *1* *[Right hand rule]:* *q+* = rule applies *directly* *q-* = rule finds opposite direction (so need to *reverse*) 1. Orient hand so *thumb* points in direction of *v* 2. Point *fingers* in direction of *field* (B) 3. Direction of *force* (Fb) is *perpendicular* to *palm*

Potential(Red) of Zn = -0.76V Potential(Red) of Cu = 0.34V What is overall cell reaction and potential?

Cu is reduced since more positive potential Cu2+ + 2e- --> Cu; *0.34V* Since reduction of Zn given but its oxidized, flip sign Zn --> Zn2+ + 2e; *0.76V* Zinc-copper cell: 0.76+0.34 = *1.10V*

Final products of electrolysis of NaCl(aq) are most likely: a. Na(s) and Cl2(g) b. HOCl(aq) and Na(s) c. Na(s) and O2(g) d. NaOH(aq) and HOCl (aq)

D

Measuring circuit values For what purpose Voltmeters vs Ammeters Internal resistance

Done to check if circuit is working, with two types of *galvanometers* - Have a coil with current to detect degree of needle deflection i. *Voltmeters* - Measure *potential difference* between *two* points - ii. *Ammeters* - Measure *current* at a particular *point* - By adding in *series* with a resistor of interest - Adding galvanos adds *internal resistance* (shunt resistance) in *parallel* >> ensures only small currents get to the meter >>> want it to be as *small* as possible

In the diagram (Press i), the electric field point A points in the positive y direction and has magnitude 5e6. (Source charge is not shown). If a particle with charge q=-3nC is placed at point A, what will be the electric force on the particle?

E(at A) = 5e6 j F(on q) = qE = *1.5e-2 -j*

A particle of mass m and charge q is placed at a point where the electric field is E. If the particle is released from rest, what is its initial acceleration?

F = ma a = F/m F = qE *a = qE / m*

In the figure below, assume that q1 = 1C, q2 -1nC, and q3 = 8C. If q4 is a negative charge, what must its value be in order for the net electric force on q2 to be zero?

F(1-on-2): pull left F(3-on-2): pull right F(4-on-2): push left Forces left must = forces right - F(3-on-2) = F(1-on-2) + F(4-on-2) F(1-on-2): 9N F(3-on-2): 18N F(4-on-2): x N x = *-9N*

Two charges, q1 = -2e-6 C and q2 = +5e-6C, are separated by a distance of 10cm. Describe the electrical force between these particles

F(e) = k [ (-q1 q2) / r² F(e) = *9N* Thus feel 9N towards each other

1. A toaster is rated at 720 W. IF it draws 6A of current, what is its resistance

Given P and I, asked for R P = I²R R = P / I² = *20Ω*

Describe combinations of capacitors How find equivalent capacitance? - parallel - series ^^ Which carry same voltage/charge

Just like with resistors, capacitors can be combined to find an *equivalent capacitance* i. *Parallel* - Same *voltage* - Sum (e.g. Ceq = C1 + C2 etc) ii. *Series* - Same *charge* - Sum reciprocals (e.g. 1/Ceq = 1/C1 + 1/C2 + 1/C3)

Three identical light bulbs are connected to a battery, as shown: What will happen if the middle bulb burns out? a. other two bulbs go out b. light intensity of the other two decrease c. light intensity of other two bulbs increase d. light intensity of other two bulbs remain same

MIddle is severed but top and bottom still function D

Describe source of magnetic fields Created by? Equation Single wire Circular loop - clockwise - counterclockwise Solenoid

Magnetic field lines created by the current *wrap* around the current B ∝ 1 /r >> increase current or closer = *stronger* magnetic field *[Single wire]:* - *thumb* point in direction of *current* - Fingers wrapping shows the *direction* of the magnetic field lines (*tt*) *[Circular loop]:* i. *Clockwise* - B points out when inside loop - B points in when outside loop ii. *Counterclockwise* - B points out when inside loop - B points in when outside loop *[Solenoid]:* - *Helical* wire shape - Field is produced *parallel* to the *central axis*, and is strongest on central axis - More *densely* tight the solenoid, the more *proportional* field is to the *current*

The figure below shows a portion of a long narrow solenoid carrying a current, I. An alpha particle is projected with a velocity down the central axis o the solenoid What is the best depiction of the direction of the magnetic force on the alpha particle?

Magnetic force is *zero*, (since parallel)

For the circuit: If the current entering the parallel combination is 12A, how much current flows through the 120-ohm resistor

Neither current is given, so we look for ratio relationships top = X bottom = 2X (since half the resistance, double gets through) Total = top + bottom Total = 2X + X = 12 X = 4A top = 4A V(top) = IR = 4A x 120Ω = *480V*

Two bar magnets are fixed in position, and a proton is projected with velocity v into the region between adjacent opposite poles What is the best depiction of the magnetic force on the proton at the shown position? [SN][SN]

Outside of magnet B points from N pole to S pole Right hand rule B points right and v downward, so F(b) = *out of plane of page (o)*

What is the current in the 100-ohm resistor shown below?

Parallel is connected directly to terminals of battery, so voltage across each is *10V* We know both V and R I = V/R = *0.1A*

The diagram shows point X held at a potential of Φ = 60V connected by a combination of resistors to a point (G) that is grounded (ground is Φ=0). What is the current through the 100-ohm resistor?

Parallel resistor = 20Ω, which is in series with 100Ω overall resistance = 120Ω potential difference = Φx-ΦG = 60 - 0 = 60V I = V /R = *0.5A*

Within a metal wire, 5e17 electrons drift past a point in 4 seconds. What is the magnitude of the current?

Q = ne = 8e-2C I = Q/t I = 8e-2 / 4s = *0.02A*

A parallel-plate capacitor with air between the plates is charged to a voltage of V=1000V by a battery. The values of Q,E, and PE are also measured. The battery is then disconnected from the capacitor and a diaelectric with constant K=4 is inserted between the plates. Which of the values will not change?

Q will not change

Whats the potential difference between the ends of a wire is 12V, the current is measured to be 0.06 A. What's the resistance of the wire?

R = V / I = *200Ω*

The Figure shows a charged parallel-plate capacitor with a uniform electric field, E, in the space between its plates. A uniform magnetic field , B, is also produced in the space between the capacitor plates by another device. At what speed would an electron need to travel between the plates in order to pass through undeflected?

RIght hand rule: Fb = downward Two forces need to equal F(e) = |q|E = eE F(b) = |q|vB = evB F(e) = F(b) *v = E/B*

For the circuit: If the current through the 10-ohm resistor is 1A,what is the current through the 20-ohm resistor?

Series = same current 1A

The battery in the circuit has an emf of 100V and an internal resistance of 5Ω. What is its terminal voltage?

The three resistors are in series is 5 + 25 + 20 = *50Ω* I = e / R = 2A V = e - Ir = *90V*

Describe alternating current Used where? How different from DC RMS voltage/current?

Unlike direct current (DC) where current runs in *one* direction AC current applies when *current changes* back and forth depending on energy needs AC generator creates *sinusoidally* varying voltage - when *positive* = flow in *one* direction - when *negative* = flow in *reverse* direction *[RMS voltage and current]:* *root mean square* is a fancy way of finding an *average* - diving a max by *√2* V(rms) = v max / √2 = *V/√2* I(rms) = i max / √2 = *I/√2*

For the circuit: If the current through the 12-ohm resistor is 1A, what is the value of the current I?

V(top) = IR = 12V >> so same for bottom since parallel I(bottom)=VR = 3A Total = bottom + top = 3A + 1A = *4A*

Describe DC circuits Voltage does what? How influence direction of current? Current equation Voltage/Current for series/parallel? Kirchoff's Law - drops - parallel Power dissipation Power from battery Energy equation Batteries resistance - charge/discharge

Voltage source *maintains* potential *difference* (voltage) between terminals - *higher* potential = (*+*) terminal (long line) - *lower* potential = (*-*) terminal (short line) Direction of current is the direction that a positive charge carriers would flow, even though negative charge carriers are actually flowing So conduction of electrons goes from (-)->(+), but the direction of current goes (+)->(-) *Current (I) = V / R* *Series resistors* - *Current* remains *same* - *Voltages* may differ *Parallel resistors* - *Voltages* must be *same* - *Currents* may differ - Current choose which path, do not go through both *[Kirchhoff's Laws]* - For a circuit with one battery as the voltage, the sum of *voltage drops* across the resistors in any complete path (starting (+) and ending (-) *matches* the voltage of the *battery* >> conservation of energy - The amount of current *entering* the *parallel* combination is equal to the *sum* of the currents that pass through all the *individual resistors* in the combination >> e.g. a circuit of 5A could look like 4A + 1A within a parallel resistor *[Power dissipated by resistor]:* - Resistors experience heat as current passes, and thus *absorb* and can radiate heat energy - *P = I²R* >> Joule heating law >> can be *summed* to get *total* dissipation Power supplied by the battery - *P = IV* Power supplied by battery *=* total power absorbed by circuit (via resistors, any other batteries, etc.) - *conversation of energy* *[Energy]:* = power x time *[Batteries]:* - Actually have some internal resistance i. If *battery supplies* to circuit (discharge) - *V = e -Ir* >> e = ideal voltage (electromotive force (emf)) >> r = internal resistance ii. If circuit supplies battery (recharging) - *V = e + Ir*

Describe superposition of electric fields Dipole +/- Net

When have two or more charges with electric fields overlap, creating one combined field. An *electric dipole* = a pair of equal but opposite charges Can take into account the vector at any point and how its direction is influenced by the two sources *E+* field vector is from *Q+* influence a point vector alone *E-* field vector from *Q-* *Net* field vector = *E_ + E+* The field is strong between the two charges (dense), and weaker as you spread out

For the following cell, what happens at the anode? Zn(s) | Zn2+ (aq) || Cl- (aq) | Cl2(g)

Zn --> Zn2+ + e-

When connecting a voltmeter to a circuit we want equivalent resistance to be as close to original as possible For the figure, if r=Rg = 10mΩ when measuring voltage across 8Ω resistor, find: a. equivalent resistance of the voltmeter and resistor b. measured voltage ~~~~~~ *IMAGINE V IN PIC IS OVER THE 8 resistor, not 5*

a. Equivalent resistance = parallel sum = *8Ω* b. Same steps to backsolve = *40V*

A uniform electric field of strength 4e6 points to the left (shown in figure). A particle of charge q=-20nC and mass m=10g is initially placed at point B. a. If the particle is released from rest, toward which point will it move and how fast will it be traveling when it arrives? b. If the particle is again placed at point B and now moved to point D, how much work is done "by the field"?

a. Negative charge feels force opposite the direction of electric field, and will move to point C. |q|E = ma a = *8m/s²* >> g --> kg v² = vo² + 2ad = *0.64m²/s²* b. W = Fdcosθ W = |q|Edcosθ θ>90o so work done by field is negative *W = -3.2e-3*

An electric dipole consists of a pair of equal but opposite charges, +Q and -Q, separated by a distance d. The dashed curves are equipotentials If a particle of mass m=1e-6 kg and charge q=n5C starts from rest at point A and moves to point B. a. How much work is done by the electric field? b. What is the speed of the particle when it reaches point B?

a. W(by E) = -ΔPE(elec) = -qΔΦ ΦA = +300V ΦB = -100V ΦA->B = (-100)-(300) = -400V -qΔΦ = *2e-6 J* b. ΔPE = ΔKE (1/2)mvB² = 2e-6 J vB = *2m/s*

Diagram shows a battery with emf of 100V connected to a circuit equipped with a switch, S. a. What is the current in the circuit when the switch is open? b. What is the current in the circuit when the switch is closed?

a. When open the 50Ω resistor is effectively out of the circuit 80Ω and 120Ω are in series = 200Ω current = V / R = *0.5A* b. All resistors are part of the circuit 80Ω in series with 120Ω = 200Ω; which is parallel to 50Ω resistance = 200x50/200+50 = 40Ω current = V / R = *2.5A*

A mass spectrometer has a source of ions that are accelerated from rest through a potential difference V and then enter a region containing a uniform magnetic field B that points out of the plane of the page and is perpendicular to the initial velocity,v, of the ion as it enters. Once an ion enters the magnetic field, it travels in a semicircular path until it strikes the detector, which records its arrival and the distance, d, from the opening a. An ion of +q and mass m will enter the field with what speed? (write in terms of q,m, and V) b. Which semicircular path would a cation follow: 1 or 2? c. If you were using this device in a lab to analyze a sample containing various isotopes of an element, how would you find the mass of a cation striking the detector if all you knew were q,v,B, and d?

a. ion loses potential energy (qV) and gains kinetic energy (1/2)mv² set equal *v = √(2qV/m)* b. Right hand rule = *downwards* - cation follows *path 2* c. centripetal force, qvB = mv² / r solve for m r=1/2 x d v = √(2qV/m) *m = qB²d² / 8V*

Homes are typically supplies with 110V (rms) a. Whats the maximum voltage? b. How much energy is used in 2 hours by a device whose resistance is 110 ohms?

a. v(max) = V/√2 V = 110V x √2 = *154V* b. Energy = power x time P = I²R = *110W* e = *0.220 kWh*

Given table of reduction potentials (Press i): a. Galvanic cell has Mg electrode and Copper. Which is anode/cathode? b. Standard cell voltage of reduction of Ag+ by Al? c. Whats the strongest reducing agent: Zn, Fe, Pd, Pd2+ d. Best approximates of cell poteial for: 2Al + 3Cu2+ --> 2Al3+ + 3Cu

a. Mg = anode; Cu = cathode b. 2.47V c. A d. -(12)(96,500)J

A proton is injected with a velocity (v) into a region of constant magnetic field (B) that points outside of the plane of the page. The direction of v is to the right in the page plane a. Describe the motion of the proton b. Find the radius of the circular trajectory it follows

a. Proton is *positively* charged Right hand rule points *down* on page plane, causing it to *curve* downwards (constant direction change) Which will continue and *repeat*, causing a rotation b. centripetal force = qvB = mv² / r = *r = mv / eB* q becomes e, since proton Fb = Fc

5 amps of current flows through an NaCl electrolytic cell for 1930 seconds, how much Na(s) and Cl2(g) is formed?

i. *Amount of electricity* Q = charge x time Q = 5amps x 1930 sec = *9650 coulombs (C)* ii. *Convert Q to moles of electrons* - Faraday constant = 1.6e-19 C/e- - Mole = 6.02e23 e-/mol = *96,500 C/mol* 9650 C x 1 mol e- / 96,500 C = *0.1mol e-* iii. *Stoich of half-reactions* (1/2):Na+ + e- --> Na; for one mole e-, make 1 mole Na (1/2): 2Cl- --> Cl2 + 2e-; for one mole e-, make 1/2 mole Cl2 = 0.1 mole Na x Mw = *2.3g* Na = 0.05 mole Cl2 x Mw = *3.55g* Cl2

*An electron is projected horizontally into the space between the plates of a parallel-plate capacitor, where the electric field has a magnitude of 56 v/m. The initial velocity of the electron is horizontal and has a magnitude of vo = 5e6 m/s* a. b. c.

pp. 1200 come after motion unit

The figure below shows a long straight wire carrying a current, I. An electron is projected above the wire and initially parallel to it What is the best description of the magnetic force on the electron at the indicated position

q- = left hand rule = F(b) *upwards*

A charge of q=-8 nC is moved from a Q=+2uC to a position thats 20cm away. What is the change in electrical potential energy?

ΔΦ = ko Q (1/rB - 1/rA) = *-9e4 V* ΔPE = qΔΦ = *7.2e-4*

In the figure, the potential for A is 1000V. What's the potential at Point B?

Φ = k (Q/r) B is twice as far as A, so should be half *ΦB=500V*