Circuit Analysis – How to Solve R-Parallel RC Circuit

circuit analysis

How to calculate the Vout when the input voltage Vin is = 20V DC + 10V AC.
Here is the circuit:

enter image description here

Best Answer

Due to some controversy, I will work the AC component of the answer two different ways.

(1) The parallel combination of the R and C is:

\$Z_{EQ} = 100 || Z_C = 100||\dfrac{1}{j2\pi(2000Hz)(8\mu F)} = 100||(-j9.95) = (0.980 - j9.85) \Omega \$

By voltage division, the AC signal is reduced by:

\$|\dfrac{Z_{EQ}}{Z_{EQ} + 100}| = 0.0976 = 9.76\% \$

Since the AC input is 10Vpp, the AC output is 0.976Vpp.

(2) Using the schematic in Olin's answer, the AC output is:

\$5V_{pp} |\dfrac{Z_C}{Z_C + 50}| = 0.976V_{pp} \$