Solving three impedances in series

circuit analysisimpedance

I have a circuit of two capacitors and three resitors, where two pairs of the components are in parallel combinations:

enter image description here

I'm trying to calculate the total impedance.

Since \$C_1\$ and \$R_1\$ are in parallel and likewise \$C_2\$ and \$R_2\$ i would think the solution would be:

\$Z_E = R_1 + \frac{1}{j\omega C_1} + R_2 + \frac{1}{j\omega C_2} + R_3\$

However my textbook tells me that the answer is what's given on the picture.

Can anyone clarify this for me? Thank you.

Best Answer

Let's translate your words into an equation for the equivalent impedance.

Since C1 and R1 are in parallel

$$Z_1 = R_1||\frac{1}{sC_1}$$

likewise C2 and R2

$$Z_2 = R_2||\frac{1}{sC_2}$$

Solving three impedances in series

$$Z_E = Z_1 + Z_2 + R_3$$