This problem have three steps please help a. To simulate the mechanical vibratio

Question

This problem have three steps please help

a. To simulate the mechanical vibration of a structure, a 10 V battery is used to charge a 470 F capacitor. The capacitor is then removed from the battery and connected to the terminals of an inductor. The circuit then oscillates and the maximum current through the inductor is 956 A. What is the value (in Henrys) of the inductance ? To make life easy, assume the components are ideal. Give your answer in the form "a.bc x 10^(x) Hr".

b. Give the frequency of the oscillations. Give your answer in the form "a.bc x 10^(x) Hz".

c.Determine the time required for the charge on the capacitor to rise from zero to its maximum value. Give your answer in the form "a.bc unit". Unit means the unit of the measurement.   (Hint: Think about what happens to the charge on the capacitor over the time required to complete one cycle of the oscillation .)

Explanation / Answer

Assume maximum inductor current and capacitor voltage are at reasonance when
1/jwC + jwL = 0 => 1-w^2 * LC = 0 => w = 1/sqrt(LC) => f = 1/2pi*sqrt(LC)

956*10^-6 * Zc = 10 => Zc = 10460.25 = 1/2pif*470e-6
f = 1/2pi*470e-6*10460.25 = 0.032 Hz = 3.20*10^-2 Hz
w = 0.2 rad/s
956*10^-6wL = 10
L = 5.23*10^4 Hr

The time required for the charge on the capacitor to rise from zero to its maximum value = 5*time constant = 5*sqrt(LC) =24.8 s

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