Given the circuit in Figure 1 and the plots of Vout (orange) and Vin (blue) in F

Question

Given the circuit in Figure 1 and the plots of Vout (orange) and Vin (blue) in Figure 2, find the value of capacitor C1. Note that V1 is a 20V (peak-to-peak) sine waveform at 1kHz. (Hint: derive either the magnitude of H(w) or the phase of H(w) and read the magnitude or phase off of the graph to solve for C1).

Given the circuit in Figure 1 and the plots of Vout (orange) and Vin (blue) in Figure 2, find the value of capacitor C1. Note that V1 is a 20V (peak-to-peak) sine waveform at 1kHz. (Hint: derive either the magnitude of H(w) or the phase of H(w) and read the magnitude or phase off of the graph to solve for C1).

Explanation / Answer

output magnitude=3 volts

capacitive impedance=Xc=1/(2*pi*1000(C1))

hence
Xc/sqrt(R1^2+Xc^2)=3/10
sqrt(R1^2+Xc^2)=10*Xc/3

R1^2+Xc^2=100*Xc^2/9
Xc=9.9449 ohm

so C1=16 uF

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