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Physics 2020 Spring 2009 Stephan LeBohec DATA SHEET - EXAM 3 SEAT # Constants: k= 1 9 2 −2 =8.99×10 N⋅m ⋅C 4 0 Electric potential: Work by operator moving a charge in an electric potential: W =q⋅V f −V i Electric field in a parallel plate capacitor: ∣= V = ∣E d 0 −19 e=1.602×10 C Q Proton =e & Q Electron=−e Electric potential from a point charge: V r =k Capacitance: C= q r q V Energy stored in a capacitor: 1 1 1 q2 2 U = q⋅ V = C⋅ V = 2 2 2C Electric cirduits: Power in an electric circuit: P=V⋅I Resistivity: R= L A Power from harmonic voltage and current: I0 V0 P=I RMS⋅V RMS with I RMS = and V RMS= 2 2 Equivalent resistance for resistors in parallel: 1 1 −1 R Parallel = R 1 R2 Equivalent capacitance for capacitors in series: −1 1 1 C Series = C1 C 2 Magnetic force: ∣=∣q∣⋅∣v∣⋅∣ Magnetic force on a charge: ∣F B∣sin Ohm's law: V =R⋅I Temperature dependence of resistivity: =0 1T −T 0 Equivalent resistance for resistors in series: R Series= R1R 2 Kirchhoff's junction rule: ∑ I IN =∑ I OUT and loop rule: ∑ V UP =∑ V DOWN Equivalent capacitance for capacitors in parallel C Parallel =C 1C 2 ∣=I⋅L∣ Magnetic force on a current: ∣F B∣sin Physics 2020 Spring 2009 Stephan LeBohec EXAM 3 Name:_____________________________________ TA (circle one): Michael A) Sarah Adam 1 Student ID #:___________________________ Isaac [33 points, 3 points per question] For each statement, circle the option you find appropriate. You do not need to show your work. 1) The electric field is always perpendicular to an equi-potential surface. TRUE FALSE 2) An equi-potential surface can not cross itself. TRUE FALSE 3) When an electron moves to a region of higher electric potential, its potential energy decreases. TRUE FALSE 4) Two light bulbs connected in series to a battery produce as much light as a single light bulb connected to the same battery. TRUE FALSE 5) A battery can deliver a fixed amount of charge in its life time. Increasing the number of light bulbs connected in series will make it last LONGER THE SAME SHORTER 6) Increasing the number of light bulbs connected in parallel will make it last LONGER THE SAME SHORTER 7) An electron moves in a straight line through a uniform magnetic field. There must be an electric field pointing in a direction perpendicular to the magnetic field. TRUE FALSE 8) Two same sign electric charges are brought together in a uniform magnetic field. When released the particles will move away from each other and stay on circular orbits. TRUE FALSE 9) An operator moves an electric charge at constant speed along a straight line perpendicular to a uniform magnetic field. The operation requires an amount of work proportional to the distance traveled. TRUE FALSE 10) An electron moves horizontally away from you in a uniform magnetic field pointing to your right. The trajectory of the electron BENDS DOWN REMAINS HORIZONATAL BENDS UP 11) A proton moves upward vertically in front of you. In order to bend its path away from you, you need to establish a horizontal magnetic field pointing TO YOUR LEFT AWAY FROM YOU TO YOUR RIGHT TOWARD YOU Physics 2020 Spring 2009 Stephan LeBohec Name:_____________________________________ TA (circle one): Michael B) 2 EXAM 3 Sarah Adam Student ID #:___________________________ Isaac [15 points] A Wheatstone bridge is a measuring instrument invented in 1833. In the circuit on the right, Rx is an unknown resistance to be measured; R1,=10Ω, R3 =40Ω and the resistance of R2 is adjustable. R2 is adjusted so VD­VB=0 at which point R2=18Ω. What is the value of Rx ? Once R 2 is adjusted V D −V C =V B −V C . Suppose the battery V provides an electromotive force V , then V D −V C =R 2⋅ and R1R 2 R2 RX V V B −V C =R X⋅ = so or R 3R X R1 R2 R3 R X R R R 2 R3 R X =R X R 1R 2 and R 2 R 3=R X R 1 so R X = 2 3 and with the given values we get R1 R X =18×40 / 10 =72 C) Two charges q 1=1.0 C and q 2=−3.0 C are positioned as indicated in the figure with w=0.60m and h=0.80m . 1) [10 points] What is the electric potential at point M ? q1 q2 and r 1M= 0.6m 20.8m2=1m so r 1M r 2M −6 −3×10−6 C 9 1×10 C V M =9×10 =−36,000 V 1m 0.6m V M =k 2) [10 points] A particle of mass m=6g and charge placed at point M and is released. What will be the final velocity of this particle? q=−3 C is The negatively charged particle in a negative electric potential has a positive 1 2 potential energy. It will move away to infinity where the potential energy will have dropped to zero so q⋅V M = m v and v= 2q⋅V m with the given numerical values, v= −6 2×3×10 C×36,000V −1 . =6 m⋅s −3 6×10 kg 2 Physics 2020 Spring 2009 Stephan LeBohec Name:_____________________________________ TA (circle one): Michael D) 3 EXAM 3 Sarah Adam Student ID #:___________________________ Isaac We consider the circuit in the figure with V 1 =1V , V 2=3V , V 3=2V , R1 =10 , R 2=20 and R 3=30 . 1) [6 points] What is the electric potential difference V A−V B ? V A−V B =−V 1−V 3=−1V−2V=−3V I1 I2 I3 2) [26 points] What is the total power dissipated in the circuit? From Kirshhoff's rules: a) I 1=I 2I 3 b) R1 I 1 R2 I 2 V 1=V 2 combining a) and c) we get d) R 1 I 1R 3 I 1−I 2V 3V 1=0 then we can c) R 1 I 1R 3 I 3 V 3V 1 =0 rewrite c) and d) as e) R 1 I 1 / R2 I 2V 1−V 2/ R 2=0 adding up e) and f) we get f) R1 R3 I 1 / R 3V 1V 3 / R3 −I 2=0 V 1−V 2 /R 2V 1 V 3 / R 3 R1 / R 2 R 1R 3 /R 3 1V−3V/20 1V2V/30 =0A . and with the numerical values we are given I 1=− 10 /20 10 30 /30 Then from e) I 2=−R1 I 1 / R 2−V 1−V 2 / R 2=−1V−3V/ 20 =0.1A . Finally from a) we have I 3=I 1−I 2=−0.1A . R1 I 1 / R2 R1 R3 I 1 / R 3V 1−V 2 /R 2V 1V 3 / R 3=0 from which The total power dissipated in the circuit is I 1=− P=R 1 I 21R 2 I 22R 3 I 23=20 0.1A230 0.1A2=0.5W