**QUESTION**

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14.12 A resistor, denoted as $R_{c}$, is connected in series with the capacitor in the circuit in Fig. 14.11(a). The new high-pass filter circuit is shown in Fig. P14.12. a) Derive the expression for $H(s)$ where $H(s)=V_{o} / V_{i}$ b) At what frequency will the magnitude of $H(j \omega)$ be maximum? c) What is the maximum value of the magnitude of $H(j \omega)$ ? d) At what frequency will the magnitude of $H(j \omega)$ equal its maximum value divided by $\sqrt{2}$ ? e) Assume a resistance of $5 \Omega$ is connected in series with the $80 \mu \mathrm{F}$ capacitor in the circuit in Fig. P14.11. Calculate $\omega_{c}, H\left(j \omega_{c}\right), H\left(j 0.125 \omega_{c}\right)$, and $H\left(j 8 \omega_{c}\right)$. Figure P14.12