A Low-Pass Filter. Figure P31.48 shows a low-pass filter (see Problem 31.47); the output voltage is taken across the capacitor in an L-R-C series circuit. Derive an expression for
Figure P31.48
Vout/Vs, the ratio of the output and source voltage amplitudes, as a function of the angular frequency ω of the source. Show that when ω is large, this ratio is proportional to ω−2 and thus is very small, and show that the ratio approaches unity in the limit of small frequency.
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