An LC circuit has zero resistance, no battery, a capacitor C=66microFarads, and

Question

An LC circuit has zero resistance, no battery, a capacitor C=66microFarads, and an inductor L=0.7H connected in a simple loop. The capacitor and inductor store a compined total energy of U=24microJoules.
(a) If all the circuits energy is stored in the capacitor at time t = 0, when is the soonest time that all the energy will be stored in the inductor?


(b) If the inductor is a cylindrical solenoid of length l=11centimeters and radius r=3centimeters, find the number of coils in the solenoid.



(c) What is the maximum magnetic field inside the inductor?

Explanation / Answer

a) In LC circuit, charge decay from capacitor follows the relation q = qmax cost.

= 1/LC . If charge on capacitor is 0, energy on it becomes 0, and total energy is transfered to inductor.

q = 0 = qmaxcost ; i.e t = n/2.

For soonest time, n = 1. Then t = /2 = 10.677 milliseconds.

b) For a solenoid, L = 0 n2 A/l.; 0 = 4 x 10^-7 H-m-1 n = no.of turns A = area of cross-section l = length of solenoid

Then n = 4655 turns

c) Maximum energy in the inductor = 24 micro joules

U = 1/2 (B2 V/ 0) V = volume of solenoid = r2l = 3.11 x 10-4 m3

Then B = 4.4 x 10-4 Tesla

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