To simulate the mechanical vibration of a structure, a 10 V battery is used to c

Question

To simulate the mechanical vibration of a structure, a 10 V battery is used to charge a 470 mu 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 966 mu 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 be times 10^4(x) H". Give the frequency ol the oscillations Give your answer in the form "abc times Hz^-

Explanation / Answer

Here,

V = 10 V

C = 470 pF = 4.7 *10^-10 F

Imax = 956 *10^-6 A

let the inductance is L

a) 0.5 * L * I^2 = 0.5 * C * V^2

L * (956 *10^-6)^2 = 4.7 *10^-10 * 10^2

solving

L = 0.0514 H

L = 5.14 *10^-2 H

the inductance is 5.14 *10^-2 H

b)

Frequency of oscillation = 1/2pi * sqrt(1/(L*C))

Frequency of oscillation = 1/(2pi) * sqrt(1/(0.0514 *4.7 *10^-10 ))

Frequency of oscillation = 32381 Hz = 3.24 *10^4 Hz

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