Question

An L-C circuit containing an 88.0-mH inductor and a 1.70-nF capacitor oscillates with a maximum current of 0.800 A

Calculate the maximum charge on the capacitor.

Calculate the oscillation frequency of the circuit

Assuming the capacitor had its maximum charge at time t= 0, calculate the energy stored in the inductor after 2.60 ms of oscillation.

Answer 1

a)

maximum energy stored in the circuit is

Umax = LI^2max / 2 = Q^2 / 2C

LI^2max / 2 = Q^2 / 2C

Q^2 = LCI^max

Q = Imax*sqrt(LC)

Q = 0.800 x sqrt(88 x 10^-3 x 1.70 x 10^-9)

Q = 9.784 x 10^-6 C

b)

the frequency of the oscillation is

f = 1 / 2pi*sqrt(LC)

f = 1 / [2pi x sqrt(88 x 10^-3 x 1.70 x 10^-9)]

f = 1.3 x 10^4 Hz

c)

the current passing through the inductor at time t is

I = Imax*sin(2pi*f*t)

the maximum energy stored in the circuit is

Umax = LI^2max / 2

Umax = L x ( Imax*sin(2pi*f*t)^2 / 2

Umax = [88 x 10^-3 x (0.800^2 x sin(2pi x 1.3 x 10^4 x 2.6 x 10^-3)] / 2

Umax = 4.1 x 10^5 J

answered by: anonymous