Question

2. LRC series circuit. [10 pts.] Consider an LRC series circuit driven by an ac voltage source Vin Vo cos(wt). (a) Derive an expression for the real ac current in the circuit in terms of L, R, C, and a. (b) Determine the resonant frequency f, and angular frequency w, by direct differentiation of the current amplitude from part (a). Compare your result to LC (c) Determine the Q factor of this circuit in terms of L, R, and C. Explain how changing each of L, R, and C affects the resonance, addressing changes in both w, and 0. For example, does alarger R make either higher, lower or no change? (d) Plot the current amplitude as a function of frequency for the specific case of L-100 mH, R = 100 Ω, C = 0.001 μF, and Vo = 1 volt. Chose a plot range appropriate to capture the resonance. Label the axes and important points including the resonant frequency, and Δω. Calculate Q for the specific values and compare to your graph. (e) Sketch phasor diagrams, including phasors for each of the circuit elements and the equivalent response, for the following situations: (i) resonance ω-a,, (ii) below resonance ω < a,, and (iii) above resonance ω > a," Be sure to label your phasors.

Answer 1

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