A 495 pF capacitor is charged to 185 V and then quickly connected to a 135 mH inductor.
Determine the frequency of oscillation. Determine the peak value of the current. Determine the maximum energy stored in the magnetic field of the inductor.
Determine the frequency of oscillation. Determine the peak value of the current. Determine the maximum energy stored in the magnetic field of the inductor.
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f =(1/2pi*LC) = 1.24e10 Hz = 12.4 GHz
Ldi/dt = V0 - Q/C = V0 - (1/C)*integral i*dt
L*d2^i/dt2 + i/C = 0 with i.c. of L*di/dt = V0 at t = 0+
Sol'n is i(t) = V0*√(C/L)sin(t/√LC) and
peak i = V0*√(C/L) = 1.12e-2A
max energy W stored in L = max energy stored in C since there is no loss mechanism, so
max W stored in L = (1/2) C V^2 = .5*495e-12*3.423e4 = 8.47e-6J
Could also get directly from 1/2 L i^2 = .5*135e-3*1.254e-4 = 8.47e-6J
Ldi/dt = V0 - Q/C = V0 - (1/C)*integral i*dt
L*d2^i/dt2 + i/C = 0 with i.c. of L*di/dt = V0 at t = 0+
Sol'n is i(t) = V0*√(C/L)sin(t/√LC) and
peak i = V0*√(C/L) = 1.12e-2A
max energy W stored in L = max energy stored in C since there is no loss mechanism, so
max W stored in L = (1/2) C V^2 = .5*495e-12*3.423e4 = 8.47e-6J
Could also get directly from 1/2 L i^2 = .5*135e-3*1.254e-4 = 8.47e-6J