Exam3_2004Spr_Solutions

Exam3_2004Spr_Solutions - Physics 8.02 TEST 3 Solutions...

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Physics 8.02 TEST 3 Solutions April 29, 2004 PLEASE DETACH THIS SHEET AND USE AT YOUR CONVENIENCE Some (possibly useful) Relations: = surface closed o inside Q ε dA E outside to inside from points dA = = b a a b b to a from moving V V V ds E C Q V U = 1 2 C V 2 = Q 2 2C d A o plate parallel κ = C τ = RC V = i R P joule = i V = i 2 R = V 2 /R 2 ˆ 4 o q r µ π × = vr B 2 ˆ 4 o I r × = ds r dB F = q v × B ext ext I dF ds B τ τ = µ µ × B = dA B ds E dt d ε = N d φ B dt L = N B i ε = L di dt / LR = U L = 1 2 L i 2 u B = | B | 2 2 0 T = 2 π ω = 1 f thru o E closed path E open surface d dI dt where d µµε =+ Φ= ∫∫ oo Bs EA Φ G G G G v Free RLC Circuit No Damping: 0 () s in ( ' ) Qt Q t ω = + , 1 ' LC = Driven LRC Circuit: if ε (t) = ε m sin( ω t ), then i (t) = i m sin( ω t - φ ), where i m = ε m R 2 + ω L – 1 ω C 2 1/2 and tan φ = ω L – 1 ω C R 1 LC XLX C ==
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8.02T Spring 2004 Exam 3 Mashup Solutions 1 Problem 1: Eight Multiple Choice Questions (24 points) Circle your choice for the correct answer to the eight questions given below. A: The three light bulbs in the circuit below are identical. What happens to the brightness of bulbs A and B when the switch is closed? (a) A stays the same, B dims (b) A brighter, B dims CORRECT (c) A and B both brighter (d) A and B both dimmer (e) A and B remain the same B. The resistors and batteries in the circuit below are all identical. Which circuit or circuits have the least power delivered to it? (1) (2) (3) (a) Circuit 1 (b) Circuit 2 (c) Circuit 3 (d) Circuit 1 = Circuit 2 CORRECT (e) Circuit 1 = Circuit 3
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8.02 Spring 2004 Exam 3 Mashup Solutions 2 C: Twelve resistors each of resistance R are hooked up so that they form a cube in the manner shown. The equivalent resistance of this arrangement for current flowing in the path indicated is (a) 3 R (b) 4 3 R (c) 5 6 R CORRECT (d) 1 3 R (e) 1 6 R The easiest way to this answer is to realize that as the current comes in by symmetry it will split into three equal currents of magnitude 3 I at the first junction. Then at the next junction it will split again equally into two currents of magnitude 6 I . Then at the next junction two of these 6 I currents will recombine into one 3 I , and three of these will recombine into a current of I as it leaves the cube, as we expect. The potential drop through this path is 5 363 6 effective III R R RR IR ++= = I , so 5 6 effective R R = D. A circuit consists of a battery with emf V, an inductor with inductance L , a capacitor with capacitance C , and three resistors, each with resistance R , as shown in the sketch. The capacitor is initially uncharged and there is no current flowing anywhere in the circuit. The switch S has been open for a long time, and is then closed, as shown in the diagram. If we wait a long time after the switch is closed, the currents in the circuit are given by: 1) 123 2 33 VV iii 3 V R === 2) 12 3 0 22 V ii i V R R == = CORRECT 3) 3 0 V i V R R = 4) 0 =
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8.02
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Exam3_2004Spr_Solutions - Physics 8.02 TEST 3 Solutions...

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