(14%) Problem 3: The values for the components of the circuit shown in the figur
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(14%) Problem 3: The values for the components of the circuit shown in the figure are V-11 V C 3.9 uF, and L 110 mH. When the capacitor is fully charged, yous switch S1 and close switch S7. ly open s2 @ ?? 25% Part (a) Find the frequency of the resulting oscillations, in hertz. @?25% Part (b) What is the maximum charge on the capacitor, în coulombs, during the oscillations? 25% Part (c) Find the maximum current through the inductor, in amperes, during the oscillations. Grade Summary lo 0% 100% Potential sin0 cotan0asinacos0 atan0 acotan sinh0 cosh0tanh cotanh0 Submissions Attempts remaining: I0 0% per attempt) detailed view 4 5 6 Degrees Radians Submit I give up! Hints: for a 0% deduction. Hints remaining: Feedback: 0% deduction per feedback. -Use the relation inductor and the inductor's inductance and current. Electromagnetic energy is conserved during the oscillations. -Equate the maximum energy stored in the magnetic field of the inductor and the maximum energy stored in the electric field of the capacitor and solve for the maximum current through the inductor -Use the formulas for the maximum energy of an inductor, in terms of its inductance and maximum cument, and for the maximum energy of a capacitor, in terms of its capacitance and maximum voltage. -Be careful with your among the energy stored in the magnetic field of the units of inductance and capacitance. 25% Part (d) What is the electromagnetic energy of the oscillating circuit, in joules?Explanation / Answer
(c) Maximum energy in the capacitor = (1/2)CV2
= (1/2)*(3.9*10-6)*112 = 235.95*10-6 J ----------(1)
Now let us consider that the amximum current in the inductor is I
therefore the maximum energy in the inductor will be
=(1/2)LI2 = (1/2)*(110*10-3)I2 --------------(2)
Now by energy conservation
Maximum energy in the inductor = Maximum energy in the capacitor
(1/2)*(110*10-3)I2 = 235.95*10-6
I = 0.0655 A
(d) Electromagnetic energy of the circuit = (1/2)CV2
= (1/2)*(3.9*10-6)*112 = 235.95*10-6 J
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