Impedance,

$\overline{){\mathbf{Z}}{\mathbf{=}}\sqrt{{\mathbf{R}}^{\mathbf{2}}\mathbf{+}{\mathbf{(}\mathbf{X}}^{}}}$_{L}_{C}

$\begin{array}{rcl}\mathbf{Z}& \mathbf{=}& \sqrt{{\mathbf{R}}^{\mathbf{2}}\mathbf{+}{\mathbf{(}{\mathbf{X}}_{\mathbf{L}}\mathbf{-}{\mathbf{X}}_{\mathbf{C}}\mathbf{)}}^{\mathbf{2}}}\\ & \mathbf{=}& \sqrt{{\mathbf{R}}^{\mathbf{2}}\mathbf{+}{(\mathrm{\omega L}-\frac{1}{\mathrm{\omega C}})}^{2}}\\ & \mathbf{=}& \sqrt{{\mathbf{83}}^{\mathbf{2}}\mathbf{+}{(737\times 112.5\times {10}^{-3}-\frac{1}{737\times 11.6\times {10}^{-6}})}^{2}}\end{array}$

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε =V_{a} - V_{b} = ε_{m}sinωt, where ε_{m} = 120 V and ω = 737 radians/second. The values for the remaining circuit components are: R = 83 Ω, L = 112.5 mH, and C = 11.6μF.

1) What is Z, the impedance of the circuit?

2) What is I_{max}, the magnitude of the maximum value of the current in the circuit?

3) What is φ, the phase angle between the generator voltage and the current in this circuit. The phase φ is defined to be positive if the current leads the generator voltage, and negative otherwise.

4) What is t_{1}, the first time after t = 0 when the voltage across the inductor is zero?

5) Which of the following statements is true?

a)The voltage across the generator is zero when the magnitudes of the voltages across the inductor and the capacitor are maximum.

b)The current in the circuit is zero when the magnitudes of the voltages across the inductor and the capacitor are maximum.

c)The magnitude of the voltage across the generator is maximum when the magnitudes of the voltages across the inductor and the capacitor are maximum.

d)The magnitude of the current in the circuit is maximum when the magnitudes of the voltages across the inductor and the capacitor are maximum.

e)There is no time when the magnitudes of the voltages across the inductor and capacitor are maximum.

6) What is V_{C} = V_{d} - V_{a}, the voltage across the capacitor, at time t = 0? Note that V_{C} is a signed number.

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