Circuit Analysis :maths using Matlab

: Circuit AnalysisConsider a circuit with an input voltage, a resistor, an inductor and TWO capacitors,as shown in figure 2.? For a general input voltage Vin formulate a system of 3 ODEs that describesthe behaviour of voltages and the current in the circuit.? Setting R = 2, C1 = 3, C2 = 4, L = 1 numerically solve the ODE system, foran input voltage Vin = 12e?0.5t(Include a plot).? Are the voltages across the two capacitors different? Explain your answer.? Solve the system with an inductance that is ten times higher (include a plot).How does the behaviour change? Explain why.? Include a copy of the MATLAB code used.? Limit the assessment to TWO A4 sized pages, using 12pt font, and marginsno smaller than 1 inch. The document should be formatted as aPDF file. The plots may go on a separate page if you run out of space.Circuit AnalysisConsider a circuit with an input voltage, a resistor, and a capacitor, as shown infigure 1.? Imagine that the input voltage initially has size 12 volts at t = 0. At t = 10 itdrops down to a value of 5 volts, which it then maintains indefinitely. SettingR = 3 and C = 2 formulate an ODE that describes the voltage across thecapacitor over time.? Solve the ODE using Laplace Transforms.? Include a plot of the solution.? What would you expect to happen to the system behavior if you increasedC? (You don?t need to re-solve, just explain your answer).? Limit the assessment to TWO A4 sized pages, using 12pt font, and marginsno smaller than 1 inch. The document should be formatted as aPDF file.Throughout the workshop we Discuss (check midcourse.net for the help you need)ed multiple types of control structures, ontheir own. For this assessment we will be combining while and if control structurestogether.? Write a pseudocode (pen and paper) algorithm that solves the ODE y0 =f(t, y) using Euler?s method.? Convert this algorithm into MATLAB syntax, as the function euler method .? Your inputs should be the start time t0, the end time tend, the function f, aninitial condition y0 and an initial step size h.? If h ? f(t, y) at any point exceeds 1, your function should halve the step sizeh.? Equally, if h?f(t, y) at any point drops below 0.01, your function should doublethe step size h.? You should also make sure that the final solution step doesn?t ?overshoot?tend. (i.e. change h during the final step to exactly reach tend).? Your MATLAB code should use the function header below, and be well-commentedwith a sensible layout.? Include your pseudocode algorithm, as well as the MATLAB code. Also includea Discuss (check midcourse.net for the help you need)ion of when the could could break, or give incorrect outputs(you DO NOT need to design your code to avoid these).? Limit the assessment to TWO A4 sized pages, using 12pt font, and marginsno smaller than 1 inch. The document should be formatted as aPDF file.

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