The values for the components of the circuit shown in the figure are V = 14 V, C
ID: 1607155 • Letter: T
Question
The values for the components of the circuit shown in the figure are V = 14 V, C = 4.3 mu F, and L = 160 mH. When the capacitor is fully charged, you simultaneously open switch S_1 and close switch S_2. Find the frequency of the resulting oscillations, in hertz. What is the maximum charge on the capacitor, in coulombs, during the oscillations? (c) Find the maximum current through the inductor, in amperes, during the oscillations. What is the electromagnetic energy of the oscillating circuit, in joules?Explanation / Answer
a)
The frequency f = 1/sqrt(L*C)
omega = 1/sqrt(0.160*4.3*10^-6) = 1205.61 rad/s
f = omega/2pi = 191.878 Hz.
b) The maximum charge = the initial charge which is voltage times the capacitance.
Q = CV = 4.3*14 = 60.2 uC.
c) The current is maximum when the charge on the capacitor is zero.
Hence the voltage across the capacitor is zero that means the energy of the capacitor is zero.
the initial energy = Q^2/2C
the energy at this point = 0.5 LI^2
hence Q^2/C = LI^2
I_max = sqrt(Q^2/LC) = (60.2*10^-6)/sqrt(0.160*4.3*10^-6) = 72.6 mA. = 0.0725 A.
d) Energy = 0.5 L I^2 = 0.5*0.160*0.0725^2 = 0.0004205 J.
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