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Question 9.88: A series audio circuit is shown in Fig. 9.88. (a) What is th...

A series audio circuit is shown in Fig. 9.88.

(a) What is the impedance of the circuit?

(b) If the frequency were halved, what would be the impedance of the circuit?

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(a) {Z}=-\mathrm{j} 20+\mathrm{j} 30+120-\mathrm{j} 20\\

\mathrm{Z}={120-\mathrm{j} 10 \Omega}\\

(b) If the frequency were halved, \frac{1}{\omega C}=\frac{1}{2 \pi f C} would cause the capacitive
impedance to double, while \omega \mathrm{L}=2 \pi \mathrm{f} \mathrm{L} would cause the inductive impedance to halve. Thus,

\begin{array}{l}{Z}=-\mathrm{j} 40+\mathrm{j} 15+120-\mathrm{j} 40 \\\\{Z}={{1} 20-\mathrm{j} 65 \Omega}\end{array}

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