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Answers to Quick Quizzes 893 6 After Joseph Priest, "Meter Resistance: Don't Forget It!" The Physics Teacher, January 2003, p. 40. points A and C. (a) Derive an equation for R x in terms of the observable resistances, R 1 and R 2 . (b) A satisfactory ground resistance would be R x * 2.00 '. Is the grounding of the station adequate if measurements give R 1 # 13.0 ' and R 2 # 6.00 '? 75. The circuit in Figure P28.75 contains two resistors, 1 # 2.00 k' and R 2 # 3.00 k', and two capacitors, C 1 # 2.00 )F and C 2 # 3.00 )F, connected to a battery with emf # 120 V. No charge is on either capacitor before switch S is closed. Determine the charges q 1 and q 2 on capacitors C 1 and C 2 , respectively, after the switch is closed. (Suggestion: First reconstruct the circuit so that it becomes a ! and that the voltage across the capacitor as a function of (c) What If? If the capacitor is fully charged, and the Answers to Quick Quizzes 28.1 (a). Power is delivered to the internal resistance of a bat- tery, so decreasing the internal resistance will decrease 28.2 (c). In a series circuit, the current is the same in all resis- tors in series. Current is not “used up” as charges pass 28.3 (a). Connecting b to c “shorts out” bulb R 2 and changes the total resistance of the circuit from R 1 % R 2 to just R 1 . Because the resistance of the circuit has decreased (and 28.4 (b). When the switch is opened, resistors R 1 and R 2 are in series, so that the total circuit resistance is larger than when 28.5 (b), (d). Adding another series resistor increases the total resistance of the circuit and thus reduces the current in 28.6 (a), (e). If the second resistor were connected in paral- lel, the total resistance of the circuit would decrease, 28.7 (a). When the switch is closed, resistors R 1 and R 2 are in parallel, so that the total circuit resistance is smaller 28.8 (c). A current is assigned to a given branch of a circuit. There may be multiple resistors and batteries in a given 28.9 (b), (d). Just after the switch is closed, there is no charge on the capacitor, so there is no voltage across it. 28.10 (c), (i). Just after the switch is closed, there is no charge on the capacitor. Current exists in both branches of the 1 2 V C # r r % R
! (1 $ e $ t/R eq C ) ε + – R 2 R 1 C 1 C 2 a b c f S d e Figure P28.75 Voltmeter S R C r ε Figure P28.76 76. This problem 6 illustrates how a digital voltmeter affects the voltage across a capacitor in an RC circuit. A digital C # dq/dt to show that this leads to the differential equation where R eq # rR/(r % R). (b) Show that the solution to this differential equation is q # r r % R C ! (1 $ e $ t/R eq C ) R eq
dq dt % q C # r r % R
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