Question

& sin(ot) A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε = Va - Vb = Emsinwt, where Em = 24 V and w = 182 radians/second. At this frequency, the circuit is in resonance with the maximum value of the current Imax = 0.95 A. The capacitance C = 110uF. The values for the resistance R and the inductance Lare unknown. + dy 1) What is L, the value of the inductance of the circuit? mH Submit 2) What is Umax,c, the value of the maximum energy stored in the capacitor during one cycle? J Submit 3) What is AU, the total energy dissipated in the circuit in one cycle? J Submit

Answer 1

The solution for this question is given below

Given, E=Emsimwt. &m=24v. W =182 rad's Imax= 0.95A C = 110x10-6F 1) w= L LC * * là cwz 110x10-6X(182)2 => L = 274145 MH 2) Maximimum energy is stored in the capacitor at I of the cycle, So, Umane e en where ella is the voltage at II seconde. » Dmax ( - 1 x C x sim ( 1) >> Umane = { CEM4x110x106x 2 4 → Umane = 1•348 10-3 ]] 5) z= Emas - VRH/WL-1 J2 >6245) = R²+(182X 2 74.45X10-3__ => R=246 = 25.262. Iman 18 2 X110X10-6 lo.951

182 3) Total energy dissipated in one cycle, AU= (Irims) ² Rot 340= (Imax)*x R x 251 => 0u = (0.95)2 x 25.26 x 20 » AU = 0.394 J 4) Q = . L = 182 X 274.45x10-3 25-26 10 = 1.9771 6) c'= 20 = 2X110 x 10-65= 220x10-6F w=182 8 = WL = . . c 2 = rew 25:26 x 220x106X182 => 0 = 0.988 So, o decreases.

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