In an oscillating LC circuit, the inductance of the inductor is L = 3 mH. The ma

Question

In an oscillating LC circuit, the inductance of the inductor is L = 3 mH. The maximum charge stored on the capacitors is 3 C, and the maximum current is 10 mA.

a. What is the energy stored in the magnetic field of the inductor when the current has its maximum value?    answer 1.5e7        
b. What is the capacitance of the capacitor?      answer 3e3
c. What is the angular frequency of oscillation?           3.33e3
d. How much time is required for the charge on the capacitor to go from zero to its maximum value?    4.71e-4

Explanation / Answer

L = 3 mH , Q = 3 C , imax =10 mA

(a) U =(1/2)Li^2 = 0.5(3*10^-3*(10*10^-3)^2

U = 1.5 *10^-7 J

(b) maxium energy stored in inductor = maximum energy stored in capacitor

U = Q^2/2C

1.5*10^-7 = (3*3)/(2*C)

C = 3*10^7 F

(c) wo =(1/LC)^1/2

wo = 1/(3*0.001*3*10^7)^0.5

wo = 3.33*10^-3 rad/s

(d) wo = 2pi/T

T = 2*3.14/(3.33*10^-3)

T = 1885.9 s

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