2004 answers Elec

2004 answers Elec - AP® Physics C: Electricity and...

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Unformatted text preview: AP® Physics C: Electricity and Magnetism 2004 Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use ® must be sought from the Advanced Placement Program . Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. This permission does not apply to any third-party copyrights contained herein. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. For further information, visit www.collegeboard.com Copyright © 2004 College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of the College Entrance Examination Board. PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service. Other products and services may be trademarks of their respective owners. For the College Board’s online home for AP professionals, visit AP Central at apcentral.collegeboard.com. AP PHYSICS C ELECTRICITY & MAGNETISM 2004 SCORING GUIDELINES General Notes about 2004 AP Physics Scoring Guidelines 1. The solutions contain the most common method(s) of solving the free-response questions, and the allocation of points for these solutions. Other methods of solution also receive appropriate credit for correct work. 2. Generally, double penalty for errors is avoided. For example, if an incorrect answer to part (a) is correctly substituted into an otherwise correct solution to part (b), full credit will usually be awarded. One exception to this may be cases when the numerical answer to a later part should be easily recognized as wrong, e.g. a speed faster than the speed of light in vacuum. 3. Implicit statements of concepts normally receive credit. For example, if use of the equation expressing a particular concept is worth one point, and a student’s solution contains the application of that equation to the problem but the student does not write the basic equation, the point is still awarded. 4. The scoring guidelines typically show numerical results using the value g = 9.8 m s 2 , but use of 10 m s 2 is of course also acceptable. 5. Numerical answers that differ from the published answer due to differences in rounding throughout the question typically receive full credit. The exception is usually when rounding makes a difference in obtaining a reasonable answer. For example, suppose a solution requires subtracting two numbers that should have five significant figures and that differ starting with the fourth digit (e.g. 20.295 and 20.278). Rounding to three digits will lose the accuracy required to determine the difference in the numbers, and some credit may be lost. Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 2 AP PHYSICS C ELECTRICITY & MAGNETISM 2004 SCORING GUIDELINES Question 1 15 points total Distribution of points (a) i. 3 points For field lines inside the shell that point outward and are reasonably close to being 90∞ to both the line charge and the shell surface, with obviously more lines on the right side than the left For field lines outside the shell that are radial and noncontinuous with those inside the shell, reasonably close to 90∞ to the shell surface, and approximately evenly spaced For no field lines inside the shell, given that there are field lines drawn elsewhere ii. 1 point 1 point 1 point 2 points For only negative charges on the inside surface of the shell, with obviously more charges on the right side For only positive charges on the outside of the shell, approximately evenly spaced 1 point 1 point Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 3 AP PHYSICS C ELECTRICITY & MAGNETISM 2004 SCORING GUIDELINES Question 1 (continued) Distribution of points (b) 4 points 4 Va 3 Vb 2 Vc 1 Vd 3 Ve For giving the lowest number to Vd (i.e. placing it at the highest potential) For giving Vc a higher number than Vd (i.e. placing it at a lower potential) 1 point For giving Vb and Ve the same number 1 point For giving the highest number to Va (i.e. placing it at the lowest potential) (c) i. 1 point 1 point 2 points Using Gauss’s law: Q Ú EidA = ε0 E Ú dA = Q ε0 For the correct expression for the value of the integral of the area A = 2 p r (where is the length of the Gaussian surface) For the correct expression for the total charge enclosed, which comes only from the line charge Q=l Substituting and solving for the field: l E (2p r ) = 1 point 1 point ε0 E= l 2pε0 r Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 4 AP PHYSICS C ELECTRICITY & MAGNETISM 2004 SCORING GUIDELINES Question 1 (continued) Distribution of points (c) (continued) ii. 2 points For any indication that the total field or the total charge enclosed is the sum of contributions from the line charge and the shell Qtot = Qline + Qshell or Etot = Eline + Eshell The field from the line charge is the same as calculated in part i. l Eline = 2pε0 r For the shell, the charge enclosed is that between r and r1 ( Qshell = r p r 2 - p r12 ) For substitution of the correct enclosed charge for the shell into Gauss’s law r Eshell ( 2p r ) = p r 2 - p r12 ε0 ( Eshell = Etot = iii. r 2ε0 r 1 point 1 point ) (r 2 - r12 ) ( r l + r 2 - r12 2pε0 r 2ε0 r ) 2 points For any indication that the total field or the total charge enclosed is the sum of contributions from the line charge and the shell Qtot = Qline + Qshell or Etot = Eline + Eshell The field from the line charge is the same as calculated in part i. l Eline = 2pε0 r For the shell, the charge enclosed is that between r2 and r1 ( Qshell = r p r22 - p r12 ) For substitution of the correct enclosed charged for the shell into Gauss’s law r Eshell ( 2p r ) = p r22 - p r12 ε0 ( Etot ( 1 point ) ) r r 2 - r12 2ε0 r 2 r l = + r 2 - r12 2pε0 r 2ε0 r 2 Eshell = 1 point ( ) Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 5 AP PHYSICS C ELECTRICITY & MAGNETISM 2004 SCORING GUIDELINES Question 2 15 points total (a) Distribution of points 1 point Once the switch is closed, VR1 = VC . From the graph, one can see that at t = 0 , VC = 0 . Therefore, all the voltage drop occurs across resistor R2 . For the correct answer, with units VR 2 = 20 V (b) 1 point 1 point From the graph, the maximum voltage across the capacitor (and thus also R1 ), is 12 V. The remaining voltage drop occurs across R2 . VR 2 = 20 V - 12 V For the correct answer, with units VR 2 = 8 V (c) 1 point 3 points A long time after the switch is closed, I C = 0 . For any indication that I R1 = I R 2 1 point Using Ohm’s law to calculate the current in R1 : I R1 = VR1 R1 = (12 V ) (15 kW ) = 0.8 ¥ 103 A Using Ohm’s law to calculate R2 : ( R2 = VR 2 I R 2 = (8 V ) 0.8 ¥ 10 -3 A ) For the correct numerical answer For the correct units R2 = 10 kW 1 point 1 point NOTE: There was a discrepancy in this question between information in the graph and the circuit diagram. The value of the time constant as shown in the graph was about a factor of ten too large when compared to the value determined from the information in the diagram. Determination of R2 by equating the expression for the time constant in terms of resistance and capacitance to the time constant from the graph yields a negative resistance. Since it was not the fault of the students that the correct analysis yielded a negative value of resistance, full credit could be earned for this method. Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 6 AP PHYSICS C ELECTRICITY & MAGNETISM 2004 SCORING GUIDELINES Question 2 (continued) Distribution of points (d) 3 points Using the relationship for the energy stored in a capacitor: 1 U = CV 2 2 For substituting the correct value of voltage For substituting the correct value of capacitance 1 2 U = (20 mF ) (12 V ) 2 For the correct answer, with correct units U = 1.44 ¥ 10 -3 J (e) 1 point 1 point 1 point 4 points For a correct value for the initial current From part (a), VR 2 = 20 V immediately after the switch is closed 1 point I max R 2 = ( 20 V ) (10 kW) = 2 ¥ 10 -3 A For a correct value for the final current From part (c), I R 2 = 0.8 ¥ 10-3 A a long time after the switch is closed 1 point For a correctly curving graph For labeling the vertical axis (including units) Only the general shape of the graph and the endpoints were graded. The time constant of the graph was not evaluated. 1 point 1 point Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 7 AP PHYSICS C ELECTRICITY & MAGNETISM 2004 SCORING GUIDELINES Question 2 (continued) Distribution of points (f) 3 points For indicating that the energy would be greater For a correct and complete explanation For example: Consider the circuit a long time after the switch is closed, when there is no current in the capacitor. If R2 is replaced with a smaller resistance, then the total resistance decreases. This results in a larger current through the resistors. Therefore, the voltage across R1 , and thus across the capacitor, increases. Since 1 U = CV 2 , energy increases. 2 One of the two explanation points could be earned for an incomplete but correct explanation. 1 point 2 points Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 8 AP PHYSICS C ELECTRICITY & MAGNETISM 2004 SCORING GUIDELINES Question 3 15 points total (a) Distribution of points 4 points The magnetic field from the wire with current I is given by: mI B= 0 (this equation can be remembered or derived from Ampere’s law) 2p r Using the equation for the flux: fm = Bid A Ú For correctly including the dimension 4 of the loop when re-expressing the area integral as an integral over r dA = 4 dr For the correct limits on the integral 4 fm = mI 0 Ú 2p r 4 dr = 2 m0 I p 4 Ú fm = 2 m0 I ln r p = 2 m0 I ( l n 4 - ln p 1 point ) For the correct answer 2 m0 I fm = ln 4 p (b) 1 point dr r For correctly performing the integration 4 1 point 1 point 3 points For correctly indicating that the induced current is counterclockwise For a complete correct explanation For example: The decreasing current means that the magnetic field, which points out of the plane of the page, is decreasing in magnitude. Using Lenz’s law, the induced current thus needs to create a field to counteract this change. The current must therefore be counterclockwise to create a field directed out of the page 1 point 2 points Only one point was awarded for incomplete explanations, such as merely saying that Lenz’s law or the right-hand rule justifies the answer. Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 9 AP PHYSICS C ELECTRICITY & MAGNETISM 2004 SCORING GUIDELINES Question 3 (continued) Distribution of points (c) 4 points For a correct relationship between the current, resistance, and derivative of the flux I loop = e R = (1 R ) ( - d f dt ) For using the expression for flux from part (a) 2 m0 I fm = ln 4 p For substituting I (t ) in the flux equation 2 m0 I 0 fm = (ln 4) e - kt p For correctly differentiating this expression to determine the emf e = - d f = - ( - k ) 2 m0 I0 (ln 4) e- kt dt p m e = 2 kp 0 I0 (ln 4) e- kt Substituting into the expression for current: 2 k m0 I 0 I loop = (ln 4) e - kt pR (d) 1 point 1 point 1 point 1 point 4 points For using a correct expression for power P = I 2R For substituting the expression for current from part (c) 2 2 2 k m0 I 0 Ê 2 k m0 I 0 P=Á (ln 4) e - kt ˆ R = Ê (ln 4)ˆ 1 e -2kt ˜ Á ˜R Ë pR ¯ Ë ¯ p For indicating that the dissipated energy is the integral of the power 1 point 1 point 1 point • U= Ú P dt 0 • 2 Ê 2 k m0 I 0 U =Á (ln 4 )ˆ 1 Ú e -2 kt dt ˜R Ë ¯ p 0 For correctly integrating the expression 2 () 1 (- 21k )(0 - 1) R Ê 2 k m0 I 0 U =Á (ln 4)ˆ 1 - 1 e -2 kt ˜ R 2k Ë ¯ p 2 Ê 2 k m0 I 0 U =Á (ln 4)ˆ ˜ Ë ¯ p 1 point • 0 2 Ê 2 m0 I 0 ˆk U =Á (ln 4)˜ Ëp ¯ 2R Copyright © 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 10 ...
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This note was uploaded on 08/05/2009 for the course PHYS 101 taught by Professor Reich during the Spring '08 term at Johns Hopkins.

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