A low-pass filter consists of a 114μF capacitor in series with a 155Ω resistor. The circuit is driven by an AC?

A low-pass filter consists of a 114μF capacitor in series with a 155Ω resistor. The circuit is driven by an AC source.

Part A: What is the crossover frequency, ( f_c )?

Part B: What is the voltage across the capacitor, ( V_c ), when the frequency ( f ) is equal to ( \frac{1}{2} f_c )?

Part C: What is the voltage across the capacitor, ( V_c ), when the frequency ( f ) is equal to ( f_c )?

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1 Answers

Jan 22, 2025

A) fc = 1/(2*pi*R*C) = 9 Hertz

C) when f= fc, Vc = 0.707(V in)

This is because Xc = R

Vc = (V in)(jXc/(R + jXc) = (V in)(j/(1+j)

|Vc| = |V in|(1/(sqrt 2) = 0.707 Vin

B) when f = 1/2(fc), Vc = 0.89(V in)

Xc = 2R

Vc = (V in)(j2/(1 +j2)

|Vc| = |V in|(2/(sqrt 5) = 0.89(V in)

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