Question

Tutorial 1: Capacitors and Inductors I. In the RC circuit of Figure 1(a), the source produces a step voltage, as discussed in lectures. The height of the step is 10V. Sketch, using a graph with labelled axes, the capacitor voltage ve as a function of time. Your sketch need not be accurate, but it should show the main features of the charging process including the voltage reached at a time equal to one time-constant, and the initial rate of increase of voltage, and it should be carefully labelled. Calculate the charge stored in the ct2 s step -10V 1% Vstep =10V 0 Figure 1

Answer 1

v_c (0^+) = 0 v_c (infinity) = 10 voltage across capacitor is given by, v_c (t) = v_c (infinity) + (v_c (0) - v (infinity)) e^-t/RC v_c (t) = 10 + (0 - 10) e^-t/1063 10^-9 v_c (t) = 10 (1 - e6-t/10 z) = 10 (1 - e6- 10^6t) Initial rate of increase of vol tax = d_vc (t)/dt Vertical-bar _t rightarrow 0 = 10^e^- 10^t Vertical-bar _t rightarrow 0 = 10^7 v/sec Time constant = RC = 10^-6 Therefore v_c (10^-6) = 10 (1 - e6- 10^6 10^- 6) = 10 (1 - e^- 1) = 10 (1 - 0.36) = 10 (0.63) = 6.3 v v_c (2) = 10 (1 -e^- 10^z) = 10 v Therefore charge stored 2 Vertical-bar _t = 2 = cv Vertical-bar _t = 2 = 1.10^-9 times 10 = 10^-8 = 10 times 10^-9 = 140 n columns at t = 2 sec