Hw18_pdf - mcconnell (kam2342) – homework18 – Turner...

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Unformatted text preview: mcconnell (kam2342) – 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 . 07 μ F capacitor is given a charge Q . After 19 s, the capacitor’s charge is 0 . 5 Q . What is the effective resistance across this capacitor? Correct answer: 391 . 589 MΩ. Explanation: Let : C = 0 . 07 μ F = 7 × 10 − 8 F and t = 19 s . The charge on the capacitor is Q ( t ) = Q e − t/τ . e t/τ = Q Q t τ = ln parenleftbigg Q Q parenrightbigg τ = t ln parenleftbigg Q Q parenrightbigg . The effective resistance is R = τ C = t C ln parenleftbigg Q Q parenrightbigg = 19 s (7 × 10 − 8 F) ln parenleftbigg Q . 5 Q parenrightbigg · 1 MΩ 10 6 Ω = 391 . 589 MΩ . 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 ”. 3 μ F 3 MΩ 7 MΩ 13 V S b a Find the voltage across the 3 MΩ center- left resistor at time t 1 = 3 s. Correct answer: 9 . 31491 V. Explanation: C R 1 R 2 V S b a Let : R 1 = 3 MΩ = 3 × 10 6 Ω , R 2 = 7 MΩ = 7 × 10 6 Ω , C = 3 μ F = 3 × 10 − 6 F , and V = 13 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 ) mcconnell (kam2342) – homework18 – Turner – (60230) 2 = (13 V) e ( − 3 s) / [(3 × 10 6 Ω)(3 × 10 − 6 F)] = 9 . 31491 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 3 MΩ center- left resistor at time t ′ = 2 . 8 s. Correct answer: 3 . 55247 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 = 3 × 10 6 Ω + 7 × 10 6 Ω = 1 × 10 7 Ω because R 1 and R 2 are in series....
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This note was uploaded on 11/22/2010 for the course PHYS 303 taught by Professor Turner during the Spring '10 term at University of Texas.

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Hw18_pdf - mcconnell (kam2342) – homework18 – Turner...

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