QP 33 In the ac RIC circuit of Fig. 1, a signal generator produces a sinusoidal input voltage Vin (t) = Avin sin(wt). We are interested here in the output voltage Vout(t) across the inductor and capacitor as shown in the figure. R L V. (H Vout (+1 in C FIG. 1: (a) The current flowing through the circuit takes the form I(t) = Io sin(wt - ). Find Io and o in terms of w, Avin, R, L, C. (b) Let About be the maximum amplitude of the output voltage Vout(t). Find the ratio Avout/ Avin in terms of w, R, L, C. (c) Find the limiting behavior of About/Avin in the following three cases: (i) w + 0, (i) w -+ oo, and (iii) w = 1/VLC. In all cases provide intuitive explanations for your results. What kind of filter does the circuit represent