For a series circuit having

PHYSICS · Multi-part · CBSE · Physics · Alternating Current · Alternating Current

Problem

For a series circuit having R=50 ΩR=50\,\Omega, L=200 mHL=200\,\text{mH} and C=5.0 μFC=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∘45^\circ can be written as ∣ωL−1ωC∣=R|\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∘+45^\circ and −45∘-45^\circ, respectively. Express each answer in rad s−1\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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