PHYS 211 Exam 2, Spring 2010

Lj} Cheek Uf @ilution be continued un the bavk (1) (10) I the thread makes an angle 0 with the verte al and is stable, determine the analytical expression of the potential difference between the plates? Tain@elqev rae Teond= mg 20 ly Dividing tan fe nig (2) (5) 1f another capacitor is with the same properties is inserted in parallel to the first, determine the new angle & of the mass as 4 function of 8 ince Al remains unchanged the new ingle Ow O (3) (8) If another capacitor is with the same properties is inserted in series to the first, determine the new angle 0 of the mass as a function of 0, Wher another capacitor is inserted in series the potential difference is divided by 2 leading tant’ tani/2 2419) . (8) Consider two remstors in parallel, determine analytically the equivalent femstor, ae (At aE eav| node | AV =IR BS BP lolol | \h°R) since then og Metis, .f$) Consider two resistors in series, determine analytically their equivalent FENIMOr, OV aol l(heh) AV = IR Ayoh+h, since “ then 4, (20) Consider the electric cireuit nas MINS - H {J Cheek if solution is continued on the back ; | In order to Solve this system we use Khirchhoff's niles: hd junction rule states Ay=J:+4; (1) where J), J and f; are the currents in 8), Ry and - » One loop rule leads to /,R»- hRyqy CoO (2) here gq; is the instantancous charge in the capacitor. It is linked to the current in the branch of the circuit by /ysdey dt » Another loop leads to -/,R, + EF « hRyO G) In order to solve this problem, we should eliminate /\ and /; as a function of 4, solve the differential equation and finally derive the results to get the various currents. + From (3) one gets /; (F -4:R2)R, when included into (1) leads to Ty( EAR YAR) * Ra) (4) « Replacing J; in Eq, (3) leads to fy. —gy/(Rog) + RoEAReg( Ry +R2))™ dgy/de which is the form of the differential equation given in the quiz with: Reg Ry (IPR TRY" a ml /RegC and b = REA Re(Ry* Ry) Jeading to ayve(ay = 1) - dyebe™ Jy is then determined using (4) and finally sy using (1). ee (b)(5) Find the final charge on the capacitor, final charge is reached as ©>!1 this means the exponential is equal to @ and 7A. (HEH Oeww 2 diagram showing the directions of the magnetic field, the magnenc Siros and the velocity and deduce the type motion the electron is having. ‘The fierce is perpendicular to the velocity ane the magnetic field: it will make the electron change its direction, which, on its Sum, changes the direction of the force. The farce is aways directed toward the center vil af the anrcular path. The magnetic force Gases. & Centmpetal acceleration, changing the: direction of the veiocity of the particle TBR) A velocity selecior uses a fixed electric field of magnitude F and the magrwetr field is varied to select particles of various energies. I a magic fice of Perpendicular to the page. A set.af directions wires are directed up out of the page, the direction of the magnetic fisid at!P is closest to the direction of 4£@ : ie @%) soit Plugs a 500 W crockpot and a 1000 W kettle into a 240 V power et operating on direct current. When we compare the two, we find Forages <Nrete 808 Repcigss < R, and Fartoot = Tisasy 808 Roptgas = Rice Frcs > H page O08 Ressctper < Recas Tcini e tige HONE RK > Ry... sae ee 5. (3%) At what rate is thermal energy being generated in the 2R-resistor when E = 12 V and R = 3.0.9? onsists of a 100 V DC power source, a 100 Q resistor, and a »sis R, which varies from 0 to100 Q. The & "i Quiz TI Fall 2009-2010 December 8, 2009 . 1. (8%) Which of the following is not a capacitance? 2. (8%) A 0.16 pF parallel-plate capacitor is charged to 10 V. Then the battery is disconnected from the capacitor. When 1.00 x 10’ positive charges of magnitude | e| are now placed on the positive plate of the capacitor, the voltage between the plates changes by a -8.9V. & <1L1V.