An LC circuit like that in the figure below consists of a 3.30-H inductor and an

Question

An LC circuit like that in the figure below consists of a 3.30-H inductor and an 838-pF capacitor that initially carries a 120-?C charge. The switch is open for

t < 0

and is then thrown closed at

t = 0.

Compute the following quantities at

t = 3.00 ms.

(a) the energy stored in the capacitor
J

(b) the total energy in the circuit
J

(c) the energy stored in the inductor

An LC circuit like that in the figure below consists of a 3.30-H inductor and an 838-pF capacitor that initially carries a 120-?C charge. The switch is open for t

Explanation / Answer

An L C circuit consits of inductor L = 3.30 H

Cpacitance of a capacitor is C = 838*10^-12 F

Initial charge of the capacitance is Qmax = 120*10^-6 C

a )

Angular frequency is, w = 1/[LC]1/2 = 1 / [3.30 * 838*10^-12]1/2 = 1.9016x104 rad/s

The charge on the capacitor at t = 3.00 ms is,

         Q = Qmaxcoswt = [120*10^-6 C]cos{1.9016x104*3x10-3} = 105.33x10-6 C

Energy stored in a capacitor is,

     E = 1/2 Q^2 /C = (105.33*10^-6 C )^2 / 2 * 838*10^-12 F = 6.62 J

b)

The total energy in the circuit is,

       E = Qmax2 / 2C = [120*10^-6 C]2 / 2*838*10^-12 = 8.59 J

C.

Energy stored in an inductor is,

E_L = 8.59J - 6.62 J = 1.97J

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