Frequency Analysis of RC Circuits

[Sastronaut]

Homework Statement

part 1. at what frequencies will the circuit act as a differentiator?
part 2. interchanging R and C of figure D produces a low pass filter. At what frequencies will v_out/v_in = .95?
part 3. at what frequencies will the RC circuit of problem 18 act as an integrator?
part 4. design a low-pass filter that has v_out/v_in =0.5 at 5kHz
part 5. for the cicuit that you designed in problem 20, at what frequencies will v_out/v_in equal .01 and .99?

Homework Equations

The Attempt at a Solution

I have completed part 1 but I am having issues in understanding where to begin for the other parts of this problem. I have attached my work and as well the circuit. any help would be greatly appreciated! thanks pf!

 

[NascentOxygen]

For part 2, you analyze the low pass filter as a potential divider, not overlooking the j term in capacitive reactance.

v(o) / (in) = v_C / ( v_R + v_C ) = 0.95

 

[Sastronaut]

Thank you nascentoxygen!