2a. To simulate the mechanical vibration of a structure, a 10 V battery is used

Question

2a. 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". 2b. Give the frequency of the oscillations. Give your answer in the form "a.bc x 10^(x) Hz".

Explanation / Answer

here,

battery , V = 10 V

capacitance , C = 4.7 * 10^-4 F

the energy stored in the capacitor , Ec = 0.5 * C * V^2

Ec = 0.5 * 4.7 * 10^-4 * 10^2

Ec = 0.0235 J

let the inductance be L

and maximum current , I = 9.56 * 10^-4 A

maximum energy of inductor = Ec = 0.0235

0.5 * L * I^2 = 0.0235

0.5 * L * ( 9.56 * 10^-4)^2 = 0.0235

L = 5.14 * 10^4 H

the inductance of the inductor is 5.14 * 10^4 H

2b)

frequency , f = 1/2pi * 1/sqrt( L*C)

f = 1/2pi * 1/sqrt(4.7 * 10^-4 * 5.14 * 10^4)

f = 3.24 * 10^-2 Hz

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