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HW 16 - benavides(jjb2356 homework 16 Turner(59130 This...

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benavides (jjb2356) – homework 16 – Turner – (59130) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A 0 . 28 μ F capacitor is given a charge Q 0 . After 1 s, the capacitor’s charge is 0 . 5 Q 0 . What is the effective resistance across this capacitor? Correct answer: 5 . 15248 MΩ. Explanation: Let : C = 0 . 28 μ F = 2 . 8 × 10 - 7 F and t = 1 s . The charge on the capacitor is Q ( t ) = Q 0 e - t/τ . e t/τ = Q 0 Q t τ = ln parenleftbigg Q 0 Q parenrightbigg τ = t ln parenleftbigg Q 0 Q parenrightbigg . The effective resistance is R = τ C = t C ln parenleftbigg Q 0 Q parenrightbigg = 1 s (2 . 8 × 10 - 7 F) ln parenleftbigg Q 0 0 . 5 Q 0 parenrightbigg · 1 MΩ 10 6 Ω = 5 . 15248 MΩ . 002 10.0 points The switch S has been in the position “a” for a long time. Then at t = 0, it is moved from “a” to “b”. C R 1 R 2 E S b a Find the time when the charge in the ca- pacitor is reduced to 1 e of its value at t = 0. 1. τ = 1 R 1 C 2. τ = R 2 C 3. τ = radicalbig R 1 R 2 C 4. τ = ( R 1 + R 2 ) C correct 5. τ = 1 ( R 1 + R 2 ) C 6. τ = 2 ( R 1 + R 2 ) C 7. τ = R 1 + R 2 2 C 8. τ = 1 R 1 R 2 C 9. τ = 1 R 2 C 10. τ = R 1 C Explanation: In charging an R C circuit, the characteris- tic time constant is given by τ = R C , where in this problem R is the equivalent resistance, or R = R 1 + R 2 .
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