Question

Example 28.12 Charging a Capacitor in an RC Circuit Problem An uncharged capacitor and a resistor are battery, as shown in Figure 28.23. If emf = 12.0 V, C = 5.00 AuF, and R = 8.00 x 105 ?, find the time constant of the circuit, the maximum charge on the capacitor, and the charge and current as functions of time. in series to a Figure 28.23 The switch in this series RC circuit, open for times t> , is closed at t = 0. Solution 0-60.0 uC 50 10 30 20 012 34 5 6 7 The time constant of the circuit is ? = RC = (8.00 × 105 ?) (5.00 × 10-6 F) = 4.00 s The maximum charge on the capacitor is 10 15.0 ?? Q-Cern/-(5.00 ?F) (12.0 V)-60.0 pC The maximum current in the circuit is emf12.0 V R 8.00 x 10,2 15.0 ?? Using these values and Equations 28.14 and 28.15 below, we find that5 )-(150)e-t/4.00 Graphs of these functions are provided in Figure 28.24 below 4(s) 012 345 6 7 Figure 28.24 Plots of (a) charge versus time and (b) current versus time for the RC circuit shown in Figure 28.23, with12.0 V, R- 8.00 x 105n, and C- 5.00 AuF At the Interactive Worked Example link at http://www.pse6.com, you can vary R, C, and and observe the charge and current as functions of time while charging or discharging the capacitor Exercise 28.12 Hints: Getting Started | I'm Stuck Now, a second resistor R2 of 2.00 × 105 ? is connected in parallel to the existing resistor in the circuit, and a second capacitor C2-2.00 is connected to the existing capacitor in parallel (a) What will be the new time constant? (b) What will be the maximum current in the circuit (leaving the battery terminal)? ? ? Now, we connect the second resistor R2 of 2.00 105 ? and the second capacitor C2 of 2.00 ÂuF both in series to the other elements of the circuit. (c) What will be the new time constant? (d) What will be the maximum current in the circuit (leaving the battery terminal)? AHA

Answer 1

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