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 mF 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 mA. 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 times 10^(x) H'. Give the frequency of the oscillations. Give your answer in the form 'a.bc times 10^(x) Hz'. Determine the time required for the charge on the capacitor to rise from zero to its maximum value during each cycle of the oscillations. Give your answer in the form 'a.bc unit.' Unit means the unit of the measurement.

Explanation / Answer

We know that in such LC circuit circuit, current will be maximum when voltage is zero,

by energy conservation,

0.5 Li^2 = 0.5 CV^2

L = CV^2/i^2

= 10^2*0.470/0.956^2

= 5.14*10^1 H

B) frequency f = w/2pi =1/((sqrt(51.4*0.470))*2pi)

= 0.0324 Hz

= 3.24*10^-2 Hz

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