A resistor denoted as $R_L$ is connected in parallel with the capacitor in the circuit in Fig. 14.7. The loaded low-pass filter circuit is shown in Fig. P14.7.
a) Derive the expression for the voltage transfer function $V_a / V_i$.
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 $10 \mathrm{k} \Omega$ is added in parallel with the 100 nF capacitor in the circuit in Fig. P14.4. Find $\omega_c, H(j 0), H\left(j \omega_c\right), H\left(j 0.1 \omega_c\right)$, and $H\left(j 10 \omega_c\right)$.
(FIGURE CAN'T COPY)