Calculating about the LC circuit

문제)

The switch is connected to position a for a long time interval. At t = 0, the switch is thrown to position b.

After this time,

(a) Calculate the frequency of oscillation of the LC circuit.

(b) Calculate the maximum charge that appears on the capacitor

(c) Calculate the maximum current in the inductor

(d) the total energy the circuit possesses at t = 3.00 s

 

풀이)

(a)

the frequency of oscillation of the LC circuit.

angular frequency  ω = 1 / √(LC), f = ω / 2π√(LC) = 1 / 2π√(1.00 × 10^-7) = 503 Hz

 

(b)

the maximum charge that appears on the capacitor

Q = CV = 1.00 μF × 12.0 V = 12.0 μC = 12.0 × 10^-6 C

 

(c)

the maximum current in the inductor

I = Q / √(LC) = 12.0 × 10^-6 C / √(1.00 × 10^-7) = 37.9 × 10^-3 A

 

(d) 

the total energy the circuit possesses at t = 3.00 s

At t = 0, energy is only in the capacitor, and total energy is conservative.

Therefore, U_total = U_capacitor + U_inductor = U_initial energy of capacitor = (CV^2) / 2 = 7.2 × 10^-5 J