In an oscillating LC circuit, L = 24.0 mH and C = 7.60 In an oscillating LC circ

Question

In an oscillating LC circuit, L = 24.0 mH and C = 7.60

In an oscillating LC circuit, L = 24.0 mH and C = 7.60 mu F. At time t = 0 the current is 9.00 mA, the charge on the capacitor is 3.10 mu C, and the capacitor is charging. What is the total energy in the circuit? What is the maximum charge on the capacitor? What is the maximum current? If the charge on the capacitor is given by q = Q cos(?t + phi ), what is the phase angle phi ? Suppose the data are the same, except that the capacitor is discharging at t = 0. What then is phi ?

Explanation / Answer

a) E = 1/2 L I^2 + Q^2/2C= 0.5*24.0E-3*9.0E-3^2 + 0.5*3.1E-6^2/7.6E-6=1.6E-6 J

b) when E = Q^2/2C

Q = sqrt(2*7.6E-6*1.6E-6)=4.93E-6 C

c) when E = 1/2 L I^2

I = sqrt( 2*1.6E-6/24.0E-3)=0.0115 A

d) so

3.1 = 4.93*cos( phi)

phi = arcos( 3.1/4.93)=309

e) 51

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