Question 9: Capacitors made from piezoelectric materials are commonly used as so

Question

Question 9:

Capacitors made from piezoelectric materials are commonly used as sound transducers ("speakers"). They often require a large operating voltage. One method for providing the required voltage is to indude the speaker as part of an LRC circuit as shown in the figure, where the speaker is modeled electrically as the capacitance C= 1.0 nF. Take R = 35 ohms and L = 55 mH. What is the resonant frequency f0 for this circuit? Express your answer using two significant figures. If the voltage source has peak amplitude V0 = 1.5V at frequency f = f0. find the peak voltage Vc0 across the speaker (i.e.. the capacitor C). Express your answer using two significant figures. Determine the ratio Vc0/v0 Express your answer using two significant figures.

Explanation / Answer

as we know in a series RLC circuit, resonant frequency is given by

1/(2*pi*sqrt(L*C))

putting the values, we get f0=21460.44 Hz=21.46 kHz

part B.

at resonance , total impedance is resistive only

so current=1.5/35=42.85 mA

capactive impedance=1/(2*pi*f0*C)=7416.2 ohms

so voltage across capacitor=capacitive impedance*current=317.78 volts

part C.

Vc0/V0=211.8

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