Part 1 Solutions Using Symbolic Math
Creating Symbolic Variables in MATLAB
1-2. The following codes create a symbolic variable ‘x’ and find the roots of the equation x2-4x+7=0:
The roots are: x=2±3 j
Using MATLAB to Solve a Simple Problem
1-2. Using symbolic variable in MATLAB, a KVL equation is solved using the following code:
The current is equivalent to the symbolic variable II. The current computed is: II=0.4068 A
Part 2 Using MATLAB to Solve Node Voltage Equations
1-2. Node voltage solution using the following equation:
1.5- VA1000-VA-3.01500=0
This equation is modelled in MATLAB using symbolic variable:
The node voltage computed is: VA=2.1 V
3-4. The node voltage equations are:
The following codes are inputted in MATLAB to solve these node voltage equations:
The computed node voltages are: VB=23.2 V, VC=21
Part 3 Exponential Response of RC Circuits
1-2. The time constant τ is computed using R*C:
In this case, the power of 10 for the capacitance value 10µF is inputted using ‘e’. The resulting time constant is: τ=10 ms
3-6. The series of time values are initialized to the variable ‘t’. Then, the capacitor and resistor voltages (Vc and Vr) are computed using the following equations:
VCt=10 1- e-tτ, VRt=10e-tτ
The following code are inputted in MATLAB to compute for the voltages and plot the results:
The resulting graph is shown in the following figure:
