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Unformatted text preview: PHYSICS 4C: QUIZ 5 SOLUTIONS Problem 1 The total voltage drop for any loop is 0, so (1) V = Q C + V R for either capacitor and either resistor. Specifically, the voltage drop over R 1 at the instant when Q 1 = 7 μ C is (2) V R 1 = V- Q 1 C 1 = 12 V- 7 μ C 1 . 8 μ F = 8 . 11V and the current through it is (3) I R 1 = V R 1 R 1 = 8 . 11V 1 . 8kΩ = 4 . 5mA Alternative solution. The equivalent resistance is R eq = 1 . 35kΩ (in par- allel, inverses of resistances add). The equivalent capacitance is C eq = 7 . 2 μ F (in parallel, capacitances add). The voltage droop over the two capacitors is the same, (4) V C = Q 1 C 1 = Q 2 C 2 = Q eq C eq , so we can solve for the charge on the equivalent capacitor: (5) Q eq = Q 1 C eq C 1 = 28 μ C Now we use the formula for charging the equivalent capacitor (6) Q eq = C eq V 1- e- t/R eq C eq , frown which we can solve for time: (7) t =- R eq C eq ln 1- Q eq V C eq = 0 . 0038s....
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- Winter '08
- Physics, Electrical resistance, Voltage drop, Ceq, Ceq Q1 Ceq, e−t/Req Ceq