exam2_sol(3)

exam2_sol(3) - PHY2049 Fall 2008 Prof. S. Hershfield Prof....

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PHY2049 Fall 2008 1 P r o f . S . H e r s h f i e l d P r o f . Y . T a k a n o P r o f . P . A v e r y Oct. 15, 2008 Exam 2 Solutions Note that each problem has three versions, each with different numbers and answers (sepa- rated by |. The numbers for each question and its correct answer are listed in order for all three versions. 1. A battery with emf 13.5 V | 14.1 V | 15.6 V is attached to a resistive rod as shown. The rod consists of two sections of the same material of equal lengths but radii r 1 = 4.9 | 5.6 | 6.5 mm and r 2 = 4.3 mm. What is the voltage across the thicker section? Answer : 5.87 V | 5.23 V | 4.75 V Solution : Because the resistors are in series, the current through each resistor is the same. Letting the re- sistances be R 1 and R 2 , i = V / ( R 1 + R 2 ), and the voltage across R 1 is V 1 = iR 1 = V [ R 1 / ( R 1 + R 2 )]. Since both resistors have the same length and are made of the same material, the resistance R = ρ L / A is inversely proportional to the area = π r 2 . Thus, 22 12 21 // R Rr r = , which can be used to evaluate () ( ) 1 112 2 1 1 / VV RRR V RR =+ = + . 2. Earth's lower atmosphere contains positive and negative ions that are produced by cosmic rays and radioactive elements in the soil. When a downward electric field of magnitude E = 1500 | 1800 | 1900 V/m is applied it acts on singly charged positive ions (number density 620 | 720 | 820 ions/cm 3 ) and singly charged negative ions (number density 330 | 520 | 470 ions/cm 3 ). If the measured current density is 1.50 × 10 12 | 1.80 × 10 12 | 2.10 × 10 12 A/m 2 , what is the average drift speed, assumed to be the same for both kinds of ions? Answer : 0.99 | 0.91 | 1.02 cm/s Solution : The positive and negative singly charged ions have drift velocities in opposite directions, so their current densities add . The net current density is thus j = e ( n + + n ) v d , where e = 1.6 × 10 19 C, n + is the number density of positive ions, n is the number density of negative ions, and v d is the average common drift speed. Solving yields v d = j / e ( n + + n )

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exam2_sol(3) - PHY2049 Fall 2008 Prof. S. Hershfield Prof....

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