Physics

Problem

For a series circuit having

R=50\,\Omega

L=200\,\text{mH}

and

C=5.0\,\mu\text{F}

connected to an AC source of variable frequency, answer the following questions. a. Part 1: (i) Show that the condition for the magnitude of the phase angle to be

45^\circ

can be written as

|\omega L - \frac{1}{\omega C}| = R

. b. Part 2: (ii) By solving the equation obtained in part (i), calculate the two angular frequencies (if any) at which the phase angle is

+45^\circ

and

-45^\circ

, respectively. Express each answer in

\text{rad}\,\text{s}^{-1}

correct to three significant figures. c. Part 3: (iii) Convert the two angular frequencies to ordinary frequencies in hertz and comment on the nature of the circuit (inductive or capacitive) at each of these frequencies. d. Part 4: (iv) Compare each frequency found in part (ii) with the resonance frequency of the circuit and explain the physical significance of your comparison.

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