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Numberade F.

Calculus 3

4 months, 3 weeks ago

even circuit diagram in the question and we have resistance value. 40 conductance is one Henry and the capacitance is 16 multiply 10 to the power minus for Jared And the source voltage is 100 costs 20. So if we compare with the standard equation then we can write that the radiant, the angular frequency Omega is going to be 10 radiant per 2nd. 10 radiant per second. Now in the question we are going to find for the current value. So I. T. That will be given by the source holds E. T. Divide the impudence of this series Rlc circuit. So for a series rlc circuit the impedance JED is given by R plus J. Omega L minus one by omega psi. Now put the values are is 40 M. So it will be 40 plus G. Multiply, Omega is 10. Multiply L is one minus one by omega psi. Omega is 10. Multiply C is 16. Multiply 10 to the power minus four. Now if you solve this then we get around 40 and this This town will be more than this. 10. So it is going to be minus. So it will be -J 52.5. This is the value of impudence. Now we can find the magnitude of the impudence that will be under road 40 square plus 52.5 and it's a square. Now if you solve this then we get approximately 66 and the phase of the impedance Z can be written as if you look at this Impedance which is 40 -J 52.5. It is in the fourth quadrant of complex numbers in the complex plane. It is in the fourth quadrant Let's suppose this is real access, this is imaginary axis. Then somewhere down this is 40 and somewhere down we have here at this point in the complex plane. So we are talking about the fourth quadrant. So the phase is going to be -10. In verse 52.5 divide 40. So it comes out to be approximately -52.64 degree. Now we can find the value of I. T. That is equal to E. T divide the impedance Z. So 80 is it is given as 100 cores 100 course 10 T divide desired can be written as a model of zero which is 60 and the phase of jed which is minus 52.64 degrees Now 100 divide 66. That comes out to be around 1.51. And this phase becomes cause Dante here in the denominator it is minus. So in the new territories it is going to be plus soap plus 52.64 degree. So we can see here that current is leading the voltage by and phase by by the Phase 52.64 degree. Now uh further indication we are going to find the value of charge charge Q. So charge Q. Is given by integration I. D. T. Integration I. D. T. So it comes out to be put the value of I so 1.51 will be out of integration. Integration cause 10 T plus 52.64 degree and DT now if you further so all this Then we get 1.51. The integration of course that is going to be 10 will be in the denominator And it is going to be signed 20 Plus 52.64°, 52.64°. So this will be the value of charge. There's 1.51 divide 10 can also be written as 0.151.

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