A High-Pass Filter. One application of L-R-C series circuits is to high-pass or low-pass filters, which filter out either the low- or high-frequency components of a sigual. Ahigh-pass filter is shown in Fig. 31.26, where the output voltage is taken across the L-R combination. (The L-R combination represents an inductive coil that also has resistance due to the large length of wire in the coil.) Derive an expression for voutlv., the ratio nf the output and source voltage amplitudes, as a function of the angular frequency cu of the source. Show that when cu is small, this ratio is proportional to cu and thus is small, and show that the ratio approaches unity in the limit oflargefrequency.

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