1At this frequency The behavior of the L-C circuit provides one example of the p

Question

1At this frequency The behavior of the L-C circuit provides one example of the phenomenon of resonance The resonant frequency is wo- what is the amplitude Vo of the voltage supplied by the current source? Express your answer using any or all of the constants given in the problem introduction. Learning Goal: To understand why a series L-C circuit acts like a short circuit at resonance An AC source drives a sinusoidal current of amplitude Io and frequency winto an inductor having inductance L and a capacitor having capacitance C that are connected in series The current as a function of time is given by I(t) = 10 sin(wt). (Figure 1) Correct Figure 1 of 1 Part E Which of the following statements best explains this fact that at the resonant frequency, there is zero voltage across the capacitor and inductor? I(t) The voltage V(t) is zero at all times because Vi, (t)--W(t). O The voltages V(t); Vi (t); and Vc(t) are zero at all times O The voltage V(t) is zero only when the current is zero The voltage V(t) is zero only at times when the current is stationary (at a max or min). Submit est Ans Activate Windows Go to Settings to activate Provide Feedback Next >

Explanation / Answer

Ans: The voltage V(t) is zero at all times because VL(t) = -VC(t).

At the resonant frequency of the circuit, the current source can easily push the current through the series L-C circuit, because the circuit has no voltage drop across it at all! Of course, there is always a voltage across the inductor, and there is always a voltage across the capacitor, since they do have a current passing through them at all times; however, at resonance, these voltages are exactly out of phase, so that the net effect is a current passing through the capacitor and the inductor without any voltage drop at all. The L-C series circuit acts as a short circuit for AC currents exactly at the resonant frequency. For this reason, a series L-C circuit is used as a trap to conduct signals at the resonant frequency to ground.

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