Solved: Filter circuit. Figure 30-33 shows a simple filte

Chapter , Problem 91

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Filter circuit. Figure 30-33 shows a simple filte r circuitdesigned to pass dc voltages with minimal attenuation andto remove, as much as possible, any ac components (suchas 60-Hz line voltage that could cause hum in a stereoreceiver, for example). Assume V[n = V1 + V2 where V1 isdc and V2 = V20 sin cot, and that any resistance is verysmall, (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,V2out5 equals (Q/C) V i, where Q is the charge on thecapacitor at any instant, and determine the amplitudeand phase of V2 out (c) Show that the attenuation of theac voltage is greatest when X c X L, and calculatethe ratio of the output to input ac voltage in this case,(id) Compare the dc output voltage to input voltage.