The network in Fig. 9.87 is part of the schematic describing an industrial electronic sensing device. What is the total impedance of the circuit at 2 kHz?
Question 9.87: The network in Fig. 9.87 is part of the schematic describing...
\begin{array}{l}\mathrm{Z}_{1}=50+\frac{1}{\mathrm{j} \omega \mathrm{C}}=50+\frac{-\mathrm{j}}{(2 \pi)\left(2 \times 10^{3}\right)\left(2 \times 10^{-6}\right)} \\\\\mathrm{Z}_{1}=50-\mathrm{j} 39.79 \\\\\mathrm{Z}_{2}=80+\mathrm{j} \omega \mathrm{L}=80+\mathrm{j}(2 \pi)\left(2 \times 10^{3}\right)\left(10 \times 10^{-3}\right) \\\\\mathrm{Z}_{2}=80+\mathrm{j} 125.66 \\\\\mathrm{Z}_{3}=100 \\\\\frac{1}{\mathrm{Z}}=\frac{1}{\mathrm{Z}_{1}}+\frac{1}{\mathrm{Z}_{2}}+\frac{1}{\mathrm{Z}_{3}} \\\\\frac{1}{\mathrm{Z}}=\frac{1}{100}+\frac{1}{50-\mathrm{j} 39.79}+\frac{1}{80+\mathrm{j} 125.66} \\\\\frac{1}{\mathrm{Z}}=10^{-3}(10+12.24+\mathrm{j} 9.745+3.605-\mathrm{j} 5.663) \\\\=(25.85+\mathrm{j} 4.082) \times 10^{-3} \\\\=26.17 \times 10^{-3} \angle 8.97^{\circ} \\\\\mathrm{Z}=38.21 \angle-8.97^{\circ} \Omega\end{array}
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