2-3 points YF12 30P033 y Notes Ask Your T An L-C circuit containing an 73.5-mH i

Question

2-3 points YF12 30P033 y Notes Ask Your T An L-C circuit containing an 73.5-mH inductor and a 1.05-nF capacitor m current of 0.718 A. (a) Calculate the maximum charge on the capacitor. (b) Calculate the oscillation frequency of the circuit. Hz (c) Assuming the capacitor had its maximum charge at time t = 0, calculate the energy stored in the inductor after 2.50 ms of oscillation. -2 points YF12 30 P041 My Notes Ask Your Tea An L-R-C circuit has L = 0.470 H, C = 2.30 × 10-5 F, and resistance R. (a) what is the angular frequency of the circuit when R = 0? rad/s (b) what value must R have to give a 5.0% decrease in angular frequency compared to the value calculated in part (a)?

Explanation / Answer

2)
a) Apply Energy conservation

UmaxC = UmaxL

Qmax^2/(2*C) = 0.5*L*Imax^2

Qmax = I*sqrt(L*C)

= 0.718*sqrt(73.5*10^-3*1.05*10^-9)

= 6.3*10^-6 C

b) f = 1/(2*pi*sqrt(L*C)

= 1/(2*pi*sqrt(73.5*10^-3*1.05*10^-9))

= 18117 Hz

c) q = Qmax*cos(w*t)

= 6.3*10^-3*cos(2*pi*18116.8*2.5*10^-3)

= 6.3*10^-6*cos(284.578)

= 1.64*10^-6 C

so, so, Energy stored in inductor = 0.5*L*Imax^2 - q^2/(2*C)

= 0.5*73.5*10^-3*0.718^2 - (1.64*10^-6)^2/(2*1.05*10^-9)

= 0.0177 J

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