Previous problem List | Next w (1 point switch In the circuit shown in the figur

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Previous problem List | Next w (1 point switch In the circuit shown in the figure above a generator supplies a voltage of EO) = 30 sinc4ovthe inductance is L= 2H, the resistance is R = 200, and 1(0) = 0. Find the current after t seconds. I(O ) = Preview My Answers Submit Answers

Explanation / Answer

Dear Student Thank you for using Chegg !! For the given RL Circuit, According to Kirchoff Voltage Law V (t) - (VR + VL) = 0 VR = IR = I (20 ) V(t) = 30 Sin (40)t VL = L dI / dt = 2 dI / dt Using these relations we get 2 dI / dt + 20 I = 30 Sin(40t) dI / dt + 10 I = 15 Sin(40t) Let d/dt be denoted by D, the auxilliary equation can be written as D + 10 = 0 D = -10 Hence General solution is CF = C1 e^(-10t) Given at t = 0, I = 0 => C1 = 0 Now to find particular integral (D + 10)I = 15 Sin (40t) I = 15 Sin (40t) / (D + 10) I = 15 Sin (40t) / (-40^2 + 10) For particular intergral replacing D with Negative of coefficient of t squared 15 Sin (40t) / (-40^2 + 10) I = 0.0094Sin (40t) Solution

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