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Question B.19: Finding the effective time constant The circuit in Fig. B.49...

Finding the effective time constant The circuit in Fig. B.49 has R_{1}=R_{2}=R_{3}=10 k \Omega \text { and } C_{1}=0.1 \mu F . Determine (a) the effective time constant τ and (b) the cutoff frequency \omega_{ O } .

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If the source is shorted, the effective resistance is the sum of R_{1} \text { and }\left(R_{2} \| R_{3}\right) ; that is,

R=R_{1}+\left(R_{2} \| R_{3}\right)=10 k +10 k \| 10 k =15 k \Omega

(a) The effective time constant is

\tau=C R=15 k \Omega \times 0.1 \mu F =1.5 ms

(b) The cutoff frequency is

\omega_{ o }=\frac{1}{\tau}=\frac{1}{1.5 ms }=667 rad / s , \text { or } 106 Hz

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