A circuit is constructed with an AC generator, a resistor, capacitor and inducto

Question

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as -va-Vb = Eqnsinut, where Enn = 24 V and = 169 radians /second. At this frequency,the circuit is in resonance with the maximum value of the current Imax" 0.82 A. The capacitance C = 159F·The values for the resistance R and the inductance L are unknown. E, sinot) R C 1) What is L, the value of the inductance of the circuit? mH Submit You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question 2) What is Umax,c, the value of the maximum energy stored in the capacitor during one cycle? J Submit You currently have O submissions for this question. Only 10 submission are allowed You can make 10 more submissions for this question

Explanation / Answer

1] L = 1/w^2C = 1/(169^2*159e-6) = 0.2202 H = 220.2 mH

2] Z = Vm/Im = 24/0.82

maximum voltage in capacitor = Vm*Xc/Z = 24*0.82/24* (1/(169*159e-6)) = 30.516 V

maximum energy = average power*T=0.5 Im^2Xc* T = 0.5*0.82^2*(1/(169*159e-6))*(2pi/169) =   0.4651 J

3] energy dissipated = average power*T = 24*0.82/2 *(2pi/169) = 0.3658 J

4] Q = Xc/R = 30.516/24 = 1.2715

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