Halliday, Resnick & Walker — Circuits: Problem 47

47 In the circuit of Fig. 27-46, \(\mathcal{E} = 1.2 \text{ kV}\), \(C = 6.5 \text{ }\mu\text{F}\), \(R_1 = R_2 = R_3 = 0.73 \text{ M}\Omega\). With \(C\) completely uncharged, switch S is suddenly closed (at \(t = 0\)). At \(t = 0\), what are (a) current \(i_1\) in resistor 1, (b) current \(i_2\) in resistor 2, and (c) current \(i_3\) in resistor 3? At \(t = \infty\) (that is, after many time constants), what are (d) \(i_1\), (e) \(i_2\), and (f) \(i_3\)? What is the potential difference \(V_2\) across resistor 2 at (g) \(t = 0\) and (h) \(t = \infty\)? (i) Sketch \(V_2\) versus \(t\) between these two extreme times.