Question

On MATLAB

Problem 1 (ME363/ME367) Analytically compute and numerically approximate the free response the following first-order, resistor- capacitor circuit, where capacitance, C-50pF (pico-Farads) and resistance, R-200ΜΩ (mega-Ohms), for an starting voltage of 2V. The voltage, v(t), represents the potential difference across the both resistor and capacitor, which are wired in parallel 1 Cv(t)v(t)-i(t) Required steps Define a time vector called t, from 0 to 0.1s with 1000 total points. Determine the time constant,T, for this system. By hand, solve for the free response of v(t) in terms of C and R Define a function (either separate .m file, or included at the bottom of the same script) that defines the first-order differential equation in the form i(t) -f(t,v). iii. iv. v.Use ODE45 to simulate the output of the function, v(t), vs. ti vi. [Figure 1] Plot v(t) (V) vs. t1 (s) with a solid blue line (linewidth-1.5). Label the axes appropriately and set the font size to 16 Add to the Figure 1, a plot of v(t) vs. t (s) determined by the analytical solution in iii. For this series, use circle data point markers and only plot 50 data points across the same time range (i.e. define a separate time vector with only 50 points) Add a legend to the figure to differential between the numerical and analytical solutions vii. viii.

Answer 1

model i90.m * 7 function f-fun1 (t, V) R-200e6 C-50e-12: end

result:

Solution for 'vitl 1.8 1.6 0.8 0.6 0.4 0.2 0.06 0.07 0.08 0.09 0.1 0.05 Timelsec] 0.01 0.02 0.03 0.04