In the LC circuit in the figure below, the inductance is L 21.8 mH and the capac
ID: 1787505 • Letter: I
Question
In the LC circuit in the figure below, the inductance is L 21.8 mH and the capacitance is c- 19.4 mF At some moment, us U 50.0 m. Capacitor initially fully charged; switch open I:0 (a) What is the maximum charge stored by the capacitor? (b) What is the maximum current in the circuit? (c) At t-o, the capacitor is fully charged. Write an expression for the charge stored by the capacitor as a function of time. (Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume Q is in coulombs and t is in seconds. Do not include units in your answer. Q(t) (d) Write an expression for the current as a function of time. (Use the following as necessary:t. Do not use other variables, substitute numeric values. Assume I is in amperes and t is in seconds. Do not include units in your answer. Assume that the positive current is in clockwise direction.)Explanation / Answer
a)
Utotal = total initial energy = UB + UE = 50 + 50 = 100 mJ = 0.1 J
C = capacitance = 19.4 x 10-3 F
Q = maximum charge on the capacitor
Utotal = (0.5)Q2/C
0.1 = (0.5)Q2/(19.4 x 10-3)
Q = 62.3 mC
b)
Utotal = total initial energy = UB + UE = 50 + 50 = 100 mJ = 0.1 J
L = 21.8 x 10-3 H
i = current
using the equation
Utotal = (0.5) L i2
0.1 = (0.5) (21.8 x 10-3) i2
i = 3.03 A
c)
Q(t) = Qo e-t/T
d)
I(t) = dQ/dt = (Qo /T) e-t/T