An industrial coil is modeled as a series combination of an inductance L and resistance R, as shown in Fig. 9.90. Since an ac voltmeter measures only the magnitude of a sinusoid, the following measurements are taken at 60 Hz when the circuit operates in the steady state:
|V_{s}| = 145 V, |V_{1}| = 50 V, |V_{o}| = 110 V
Use these measurements to determine the values of L and R.
From (1) and (2)
\begin{array}{l}\frac{50}{110}=\frac{80}{|\mathrm{R}+\mathrm{j} \mathrm{X}|} \\\\|\mathrm{R}+\mathrm{j} \mathrm{X}|=(80)\left(\frac{11}{5}\right) \\\\\mathrm{R}^{2}+\mathrm{X}^{2}=30976\end{array}From (1)
|80+\mathrm{R}+\mathrm{j} \mathrm{X}|=\frac{(80)(145)}{50}=232\\\\ \begin{array}{l}6400+160 R+R^{2}+X^{2}=53824 \\\\160 R+R^{2}+X^{2}=47424\end{array}Subtracting (3) from (4)
160 \mathrm{R}=16448 \longrightarrow \mathrm{R}={102.8} \Omega\\\\From (3)
\begin{array}{l}X^{2}=30976-10568=20408 \\\\X=142.86=377 \mathrm{L} \longrightarrow \mathrm{L}=0.3789 \mathrm{H}\end{array}