1. What is the capacitance of an oscillating LC circuit if the maximum charge on
ID: 1451430 • Letter: 1
Question
1. What is the capacitance of an oscillating LC circuit if the maximum charge on the capacitor is 1.20 C and the total energy is 154 J?
2. LC oscillators have been used in circuits connected to loudspeakers to create some of the sounds of electronic music.
What inductance must be used with a 7.30 F capacitor to produce a frequency of 10.0 kHz, which is near the middle of the audible range of frequencies?
3.A 264.0 mH inductor is connected across the output terminals of an AC generator that is delivering an output voltage of 113.0 mV rms. What is the alternating current through the inductor if the frequency of the emf is 0.070 kHz?
What is the alternating current if the frequency of the generator is changed to 0.95 kHz?
Explanation / Answer
1) Apply, Umax = Q^2/(2*C)
==> C = Q^2/(2*Umax)
= (1.2*10^-6)^2/(2*154*10^-6)
= 4.68*10^-9 F
2)
we know, f = 1/(2*pi*sqrt(L*C))
f^2 = 1/(4*pi^2*L*C)
L = 1/(4*pi^2*f^2*C)
= 1/(4*pi^2*(10*10^3)^2*7.3*10^-6)
= 3.47*10^-5 H
3)
when f = 0.070 khz = 70 hz
inductive reactance, XL = 2*pi*f*L
= 2*pi*70*0.264
= 116.1 ohms
so, Irms = Vrms/XL
= 113 mV/116.1
= 0.973 mA
when f = 0.95 khz = 950 hz
inductive reactance, XL = 2*pi*f*L
= 2*pi*950*0.264
= 1576 ohms
so, Irms = Vrms/XL
= 113 mV/1576
= 0.072 mA
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