18 - Kapoor (mk9499) homework18 Turner (60230) 1 This...

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Unformatted text preview: Kapoor (mk9499) homework18 Turner (60230) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A 0 . 26 F capacitor is given a charge Q . After 12 s, the capacitors charge is 0 . 5 Q . What is the effective resistance across this capacitor? Correct answer: 66 . 5859 M. Explanation: Let : C = 0 . 26 F = 2 . 6 10 7 F and t = 12 s . The charge on the capacitor is Q ( t ) = Q e t/ . e t/ = Q Q t = ln parenleftbigg Q Q parenrightbigg = t ln parenleftbigg Q Q parenrightbigg . The effective resistance is R = C = t C ln parenleftbigg Q Q parenrightbigg = 12 s (2 . 6 10 7 F) ln parenleftbigg Q . 5 Q parenrightbigg 1 M 10 6 = 66 . 5859 M . 002 (part 1 of 2) 10.0 points For a long period of time the switch S is in position b . At t = 0 s, the switch S is moved from position b to position a . 4 F 2 M 6 M 16 V S b a Find the voltage across the 2 M center- left resistor at time t 1 = 3 s. Correct answer: 10 . 9966 V. Explanation: C R 1 R 2 V S b a Let : R 1 = 2 M = 2 10 6 , R 2 = 6 M = 6 10 6 , C = 4 F = 4 10 6 F , and V = 16 V . When the switch is closed to position a , the resistor R 2 is not part of the circuit and may be disregarded, see Figure (a). C R 1 V Figure ( a ) For an RC circuit, I = I e t/ ( R C ) = parenleftbigg V R 1 parenrightbigg e t/ ( R 1 C ) . Because I R 1 = V R 1 , we have V R 1 = V e t 1 / ( R 1 C ) Kapoor (mk9499) homework18 Turner (60230) 2 = (16 V) e ( 3 s) / [(2 10 6 )(4 10 6 F)] = 10 . 9966 V . 003 (part 2 of 2) 10.0 points Much later, at some time t = 0 s, the switch is moved from position a to position b . Find the voltage across the 2 M center- left resistor at time t = 2 . 7 s. Correct answer: 3 . 67635 V. Explanation: Now the switch moves to position b , thereby excluding the battery from the cir- cuit, see Figure (b). C R 1 R 2 Figure ( b ) Note: The equivalent resistance of the cir- cuit is R eq = R 1 + R 2 = 2 10 6 + 6 10 6 = 8 10 6 because R 1 and R 2 are in series....
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18 - Kapoor (mk9499) homework18 Turner (60230) 1 This...

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