Find the current i(t) in an LCR-circuit with R = 11 ohms, L = 0.5 henry and C = 10?2 farad, which is connected to a source of EMF E(t) = sin(120?t). Assume that initially the current and capacitor charge are zero.

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When a series RLC circuit where the resistance value R. is equal to 11. The inductions L. Is equal to 0.5. Henry and capacitance C. Is equal to tend to the power minus two ferrets and the source of all it is E. D. In the function of time that is given as a sign 120 T. From here. If we compared with the standard equation sine omega T. Then we can say that value of omega, the angular frequency that comes out to be 1 20 radiant per second. Now in the kitchen we are going to find the current value I. T. So current will be equal to the voltage, the source voltage, divide the impedance Z. Now first we will find the value of impedance Z. L. Sorry the value of impudence that let's suppose this is our equation first. So in series rlc circuit the impudence is given by R plus G. Omega L -1 by Omega Psi. So put the values zero equal to 11 plus J. Omega is 1 20 multiply L 0.5 minus one, divide 1 20 multiply 10 to the power minus two for them. If you solve this then we get 11 plus J multiply 59.16. This is the impedance in complex form. From here we can find the angle and the magnitude of this impotence. So modoff said that will be under root 11 square plus 59.16 and it's a square. Now if you solve this then we get around 60.17. This will be the impudence of this given RLC circuit. And the phase Of this impotence said that will be 10 in worse. The Imaginary component of the complex number Z. That is 59.16, divide the real part which is 11. So it comes out to be 10 in worse. 5.37. That is approximately equal to 79 four or 5 degree. So I. T. From the equation first we can write I. T. Will be E. T divide zero. So that can be written as E. T. The mode of zero and the face of zero. This impotence that can be written as the magnitude of that multiply its face. So we can right here sign 1 20 T divide models that is 60.17 and the phase is 79.45 degrees. So from here I can write value of fight is going to be One Divide 60.17. That can be written as 16.6. Sign 1 2080 -79.45°. And this will be in Milli ampere

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