Question

3. In the figure, the battery has an emf of 12.0 V, the inductance is 2.81mH and the capacitance is 9.00 pF. The switch has been set to position a for a long time so that the capacitor is charged. The switch is then thrown to position b, removing the battery from the circuit and connecting the capacitor directly across the inductor. a. Find the frequency of oscillation of the circuit. b. What are the maximum values of charge on the capacitor and current in the circuit? €

Answer 1

Solution: 3. a) The frequency 4 osoitlation in the vivonit is given by, fE 271 VLO using, L = 2.8.1 mitt = 2.81 X103 H f c = 9:00 pF = 9.00 pF = 9.00 x 10-12 F # Bruce 21 VLC 2TT V2.81 X10-3 x9.00 x10-12 = 1:00088106 42 1.0008 MHz The frequency of oscillation of the circuit is, f = 1.0008 8106 Hz 1.0008 MHZ (Auswers). leeee E- . a to (ob). Ret, initially a capacitor C is changed by connecting it to a sowie of voltage ou battery of lif & = 12.0V by comeeting the switch s to position a. Now, the switch s is thrown from perition to position b. As a result, the source on battery is cut off & the change stored on the capaciten e begins ins to discharge through a inductors, L. Let, of be instantaneous change on a fin de be the castantaneous current in the circuit. Hence, the instantaneous emif equation of the ciscuit is, L di + 9 = + 2 = 0 o on, Ld2q atz where, > (2) en, d2q 112 + Wo e q = 0 wo? - t

The general Volution of eqı(2) , 9 = A Coswot t f Sin Wot > (3) where, A & B are two apbitrary constant. To find- there constants we apply the initial conditions that, at q=% = cv = 0 wring, at t= 0,9 =% en eq. (3) we ostain, 20 = A → A = 20 > (4) & at t=0, dq t=0 in eq.(3) 0. at 29 = - A wo sin Not to wo Coswot at o = B wo B=0 > (S) the values of Af B in eq (3) we obtain, q=% Cos Not . using q may The maximum value of change on the capaciton =% CV = 9.00 8 10 12 x 12 = 108 X10 qmas = 1.08 * 10-10 e -12 (Answers) Sin wot The cument in the cincuit is, - dq - - % wo dt .. The maximum value of cument in the circuit is, imax % wo = CV NLC = 1.08 x 10 10x 6.29 X106 6.79 x 10-4 = 6·79 810-1 A imax