Time Constant of a Complex RC Circuit
Can I just take the resistances in series and the capacitances in parallel?


That would not be possible as \$C_1\$ and \$C_2\$ are not in parallel and \$G\$ and \$R_s\$ are not in series.

The most "simple" way would be to use regular parallel/series formula's to calculate the total equivalent impedance.

$$R_{series} = R_1 + R_2$$
$$R_{parallel} = R_1//R_2 = \frac{R_1R_2}{R_1+R_2}$$

So this would give you something along the lines of

$$\begin{align}
Z &amp;= (\frac{1}{G}//\frac{1}{C_1s} + R_s)//\frac{1}{C_2s}\\
&amp;= \left[\left(\frac{1}{G+C_1s} + R_s\right)^{-1} + C_2s\right]^{-1}
\end{align}$$

Alternatively, you can also use 2-EET (extra-element theorem) to get the time constants. Let's say \$G = \frac{1}{R}\$.

$$Z = Z^{(dc)}\frac{1 + \frac{Z_{n1}}{Z_1} + \frac{Z_{n2}}{Z_2} + \frac{Z_{n1}}{Z_1}\frac{Z_{n2}^{(1)}}{Z_2}}{1 + \frac{Z_{d1}}{Z_1} + \frac{Z_{d2}}{Z_2} + \frac{Z_{d1}}{Z_1}\frac{Z_{d2}^{(1)}}{Z_2}}$$

Where each of these terms is actually quite easy to find if you know the method (\$Z_1 = \frac{1}{C_1s}\$ and \$Z_2 = \frac{1}{C_2s}\$). We find

$$\begin{align}
Z^{(dc)} &amp;= R + R_s\\
Z_{n1} &amp;= R//R_s\\
Z_{n2} &amp;= 0\\
Z_{n2}^{(1)} &amp;= 0\\
Z_{d1} &amp;= R\\
Z_{d2} &amp;= R + R_s\\
Z_{d2}^{(1)} &amp;= R_s
\end{align}$$

So plugging these in you get

$$\begin{align}
Z &amp;= \left(R + R_s\right)\frac{1 + (R//R_s)C_1s}{1 + RC_1s + (R+R_s)C_2s + RR_sC_1C_2s^2}\\
&amp;= \frac{A}{1 + \tau_1s} + \frac{B}{1 + \tau_2s}
\end{align}$$

You have two time constants in this circuit at the roots of the denominator. If these time constants are expected to be far apart, you can use a common approximation:

$$\begin{align}
d(s) &amp;= 1 + as + bs^2\\
\tau_1 &amp;\approx a\\
\tau_2 &amp;\approx \frac{b}{a}
\end{align}$$

(it is an assumption that if \$s\$ is small then \$s^2\$ is much smaller. If that makes \$as \gg bs^2\$ then \$bs^2\$ is negligible).

You can then approximate the dominant (slowest) time-constant using

$$\tau_1 \approx RC_1 + (R+R_s)C_2$$

You should always verify by approximating \$\tau_2\$ as well and then checking that it is much smaller. If it isn't you'll have to solve the quadratic equation.