Consider the LC circuit in the figure below. At t = 0, the current is I = 34 mA

Question

Consider the LC circuit in the figure below. At t = 0, the current is I = 34 mA and the charge q on the capacitor is zero. (Assume C = 3,050 pF, and L = 16 mH.

(a) What is the energy stored in the inductor at t = 0?

__________J

(b) At some instant t1, the current will be zero. What is the charge on the capacitor at t1?

__________C

(c) Find t1. (There are many possible values of t1; find the one closest to t = 0.)

__________s

(d) Using the value of t1 from part (c), find the magnitudes of I and q at t = 3t1.

I = __________ A

q= __________ C

Explanation / Answer

given

at t = 0, I = 34 mA = 0.034 A

C = 3050 pF = 3.05*10^-9 F

L = 16 mH = 0.016 H

a) at t= 0,

UL = 0.5*L*I^2

= 0.5*0.016*0.034^2

= 9.25*10^-6 J

b) Apply conservation of energy

Q^2/(2*C) = (1/2)*L*I^2

==> Q = I*sqrt(L*C)

= 0.034*sqrt(0.016*3.05*10^-9)

= 2.38*10^-7 C

c) angular frequency, w = 1/sqrt(L*C)

= 1/sqrt(0.016*3.05*10^-9)

= 1.43*10^5 rad/s

it hapens at t = T/4

= (2*pi/w)/4

= pi/(2*w)

= pi/(2*1.43*10^5)

= 1.1*10^-5 s

d) I = 0 A

Q = 2.38*10^-7 C

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