RC CIRCUITS:
Assume that capacitor is completely discharged when t<0. Plot these graphs in MATLAB or any other computing software that you are comfortable with.
For the RC circuit in the figure:
1) Hand find out the expression for the voltage and current of the capacitor and plot these equations by using MATLAB.
2) Plot the capacitor voltage and current for R=100Ohm and C = 1µF, R = 1k and C = 800mF and comment about the differences you see in the graphs.
3) find out the time constants of each circuit and point out this time constants at your voltage graphs.
4) Hand find out the expression for the voltage and current of the resistor and plot these equations by using MATLAB.
5) Assume the output is taken from the capacitor in this RC system with R=100Ohm and C=1µF. Plot the step and impulse response of the system by using the LSIM (you can use TF function before LSIM to find out your system coefficients) function of MATLAB.
6) Assume the output is taken from the capacitor in this RC system with R = 100 Ohm and C = 1µF. This RC system is a first order low pass filter with a break frequency. find out the break frequency for this system.
7) Apply two ac signals (x1(t) and x2(t))to your system by using LSIM function of MATLAB. X_{1}(t) is a sinusoidal signal with 500 Hz frequency and x_{2}(t) is a sinusoidal signal with 100 Hz frequency. You will notice different effects of your RC system (low pass filter) to these signals.
What is the reason for this difference.