The circuit shown in Figure P 13.4-11 shows an experimental setup that could be used to

QUESTION:

The circuit shown in Figure P 13.4-11 shows an experimental setup that could be used to measure the parameters k, Q, and \(\omega_0\) of this series resonant circuit. These parameters can be determined from a magnitude frequency response plot for \(\mathbf{Y}=\mathbf{I} / \mathbf{V}\). It is more convenient to measure node voltages than currents, so the node voltages \(\mathbf{V}\) and \(\mathbf{V}_2\) have been measured. Express \(|\mathbf{Y}|\) as a function of \(\mathbf{V}\) and \(\mathbf{V}_2\)

Hint: Let \(\mathbf{V}=A\) and \(\mathrm{V}_2=B \angle {\theta}\).

Then \(\mathbf{I}=\frac{(A-B \cos \theta)-j B \sin \theta}{R}\)