Question

Problem 8.66 7 of 16 Part A Suppose the circuit in (Figure 1), has a 4.8 nH inductor and a 3.0 pF capacitor Calculate the frequency, in GHz, of the sinusoidal output for t 0 Express your answer using three significant figures. GHz Figure 1 of 1 Subnit Part B The dc voltage source and series-connected resistor in the figure, are used to establish the initial energy in the inductor. If V 10 V and R 37 Ω . calculate the initial energy stored in the inductor に0 L. Express your answer to three significant figures and include the appropriate units. (0)Value Units

Answer 1

For + 20, the switch is at position 'b' the circuit for t greaterthanorequalto 0 is For t greaterthanorequalto 0, circuit is LC circuit therefore for an LC circuit we have w^2_0 = 1/LC rightarrow w_0 = 1/squareroot LC w_0 = 2pi f_0 f_0 = 1/2pi squareroot LC L = 4.8 nm c = 3.08 F f_0 = 1/2pi squareroot (4.8 times 10^-9)(3 times 10^-12) f_0 = 1.326 GHz (b) For t < 0, switch is at position 'a' and circuit is under steady state therefore capacitor acts as an open circuit and inductor is short circuit The circuit at t = 0 is iL() = V/R = 10/37 = 0.27 A Inductor doesn�t allow sudden charge of current therefore iL() = iL () = 0.27 A Initial energy stored in inductor is w(0) = 1/2 Li_L (0)^2 w(0) = 1/2 (4.8 times 10^-9)(0.27)^2 w(0) = 0.175 nJ (c) For t greaterthanorequalto 0 circuit