$\text{R}_c$
$C$
$C$
$+$ \newline $v_i$
$+$ \newline $R$
$v_o$
Consider the circuit in the above figure.
(a) Find the transfer function from $v_i$ to $v_o$.
(b) Determine the cut-off frequency in terms of the circuit elements.
(c) Let R = 40 k$\Omega$, C = 2.5 nF. Find $R_c$ for which the cut-off frequency is 8000 rad/s.