Example 28.12 Charging a Capacitor in an RC Circuit Problem An uncharged capacitor and a resistor are connected in series to a battery, as shown in Figure 28.23. If emf = 12.0 V, C = 5.00 µF, 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. R w Solution The time constant of the circuit is T= RC = (8.00 x 10 2) (5.00 x 10-6 F) = 4.00 s The maximum charge on the capacitor is Q=Cemf = (5.00 μF) (12.0 V) = 60.0 μC The maximum current in the circuit is cmf 12.0 V 15.0 με R 8.00 × 10% 52 60 Figure 28.23 The switch in this series RC circuit, open for times t> 0, is closed at t = 0. 50 40 30 20 10 0 01 2 3 4 567 (a) JuA) 15 10 (s) Q-60.0μC 10-15.0μA Using these values and Equations 28.14 and 28.15 below, we find that (t)=(60.0 μC) (1-/4.00 s) 1(t)=(15.0 A)/4.00 s Graphs of these functions are provided in Figure 28.24 below. 5 0 1 2 3 4 5 6 7 (b) 1(s) Figure 28.24 Plots of (a) charge versus time and (b) current versus time for the RC circuit shown in Figure 28.23, with = 12.0 V, R = 8.00 x 1050, and C = 5.00 µF. Exercise 28.12 Hints: Getting Started | I'm stuck Now, a second resistor R2 of 5.00 x 105 is connected in parallel to the existing resistor in the circuit, and a second capacitor C2 = 3.00 µF is connected to the existing capacitor in parallel. (a) What will be the new time constant? S (b) What will be the maximum current in the circuit (leaving the battery terminal)? Imax = ÂμA Now, we connect the second resistor R2 of 5.00 x 105 2 and the second capacitor C2 of 3.00 AuF both in series to the other elements of the circuit. (c) What will be the new time constant? T = S (d) What will be the maximum current in the circuit (leaving the battery terminal)? Imax = ÂμA