Chapter 30, Problem 91GP

Filler circuit. Figure 30–33 shows a simple filler circuit designed to pass dc voltages with minimal attenuation and to remove, as much as possible, any ac components (such as 60-Hz line voltage that could cause hum in a stereo receiver, for example). Assume V_in = V₁ + V₂ where V₁ is dc and V₂ = V₂₀sin ωt, and that any resistance is very small. (a) Determine the current through the capacitor give amplitude and phase (assume R = 0 and X_L > X_C). (b) Show that the ac component of the output voltage, V_{2 out}, equals (Q/C) − V₁, where Q is the charge on the capacitor at any instant, and determine the amplitude and phase of V_{2 out}. (c) Show that the attenuation of the ac voltage is greatest when X_C ≪ X_L, and calculate the ratio of the output to input ac voltage in this case. (d) Compare the dc output voltage to input voltage.

FIGURE 30–33

Problems 91 and 92.