Question

In an oscillating LC circuit in which C = 4.4 PF, the maximum potential difference across the capacitor during the oscillations is 1.9 V and the maximum current through the inductor is 41.7 mA. What are (a) the inductance L and (b) the frequency of the oscillations? (c) How much time is required for the charge on the capacitor to rise from zero to its maximum value? (a) Number Units Units (b) Number (c) Number Units

Answer 1

here,

C = 4.4 uF = 4.4 * 10^-6 F

maximum potential differnce , V = 1.9 V

the maximum current , I = 41.7 mA = 0.0417 A

a)

let the inductance be L

using conservation of energy

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

L * 0.0417^2 = 4.4 * 10^-6 * 1.9^2

solving for L

L = 9.13 * 10^-3 H

the inductance is 9.13 * 10^-3 H

b)

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

f = 1/2pi * 1/sqrt(9.13 * 10^-3 * 4.4 * 10^-6)

f = 7837 Hz

c)

the time taken , t = Time period /4

t = (1/7837 /4)

t = 3.2 * 10^-5 s