Integral Institution Professor Course Date ABSTRACT To derive a equation that satisfies the damped and undamped condition in an RLC circuit using the complex differential analysis. Here an RLC circuit is taken and the flow of current is maintained constant. When under a damped condition and underdamped condition the flow of current with respect to time is computed. The resulting two roots of the equation is used to derive the condition for a damped oscillation in a RLC circuit. Apart from this other small derivations and explations are provided wherever there is a possibility. Proof( theory) Consider the following circuit diagram. Here a Resistor R a capacitor C and inductor L are connected in series. This circuit is called as RLC circuit. Allow the current to flow through it at time t=0. Assume a constant electromotive force is being supplied to the RLC circuit with a potential E. Then the the amount of charge flowing throuigh the RLC circuit. This is evident from the formula that Q=It where the small change in dQ= Idt. When dQ/dt = I then ∫Idt = Q. This result is exploited in the above problem to find the value of Q from the current that is flowing in a RLC circuit. Integrating i for the circuit in problem 7 i = -77.9 e-1.01t 77.9 + 77.9 e-0.155tA =∫-77.9 e-1.01t +∫77.9 e-0.155t Let u =-1.01t let u = -0.155t du =1.01dt du =0.155t = -77.9 (eu) + 77.9 (eu) = e -1.01t – e-0.155t Q =77.1 e-1.01t – 503 e-0.155t +(503-77.1) Hence Q = 77.1 e-1.01t -503 e-0.155t +426C. Bibiliography SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS. In Differential analysis (pp. L1-L2). Wiley. Paul's online maths note. Retrieved August 8 2017 from tutorial.math.lamar.edu Interactive Mathematics. Retrieved from www.intmath.com Outline of Advanced Calculus (3rd ed.). Tata McGraw Hills. [...]
SO the questions that needs to be done are 16, 8 and 6. Please have a look at the pdf first because it shows the format and the requirements of the whole project.