Maple/Example/CAD Fig 03 14

This page goes over how to get the equations from and solve the circuit in Figure 3-14 of "Circuit Analysis and Design" by Ulaby, Maharbiz, and Furse.

Convert to Symbols

For the Maple worksheet, we are going to use symbols for each of the circuit elements. The 6 V source will be $$v_1$$ and the 4 V source will be $$v_2$$. For the resistors, label each with a subscript that matches the value in ohms (e.g. the 6 $$\Omega$$ resistor will be called $$R_6$$.

Initialization

Go ahead and put

restart

as the first executable in your worksheet.

Define Equations

To solve this circuit using Mesh Current Method, note that there are three meshes and no current sources so you have three independent KVL equations. While there are six loops to choose from, there is no reason to not just choose the three meshes. If you start at the lower-left hand corner of each mesh and count the voltage drops clockwise, you get:

\( \begin{align*} KVL,l1&=-v_1+R_2I_1+R_3(I_1-I_2)+R_6(I_1-I_3)+v_2=0\\ KVL,l2&=R_3(I_2-I_1)+R_4I_2+R_5(I_2-I_3)=0\\ KVL,l3&=-v_2+R_6(I_3-I_1)+R_5(I_3-I_2)+R_7I_3=0 \end{align*} \)

You can add those to your Maple worksheet with:

KVLl1 := -v1 + R2*I1 + R3*(I1 - I2) + R6*(I1 - I3) + v2 = 0;
KVLl2 := R3*(I2 - I1) + R4*I2 + R5*(I2 - I3) = 0;
KVLl3 := -v2 + R6*(I3 - I1) + R5*(I3 - I2) + R7*I3 = 0;

Solve Equations

You now want to solve the equations for the mesh currents; you can get the solutions (and store them) with the code:

soln1 := solve({KVLl1, KVLl2, KVLl3}, [I1, I2, I3])

In the example worksheet, the solutions are printed out. You should generally run this command at least once without putting a : at the end to make sure you are actually getting a set of solutions and not just an empty list. Once you have confirmed that you are getting a solution, if you do not need to see the full symbolic solutions, you can then add a : to the end of this line to suppress printing.

Make Substitutions

Now that you have symbolic answers, you can make numerical substitutions for those symbols using the subs command. The subs command expects a series of equalities to define the substitutions followed by a single item into which to make those substitutions. For example, to see what x is when d is 10, you can write:

subs(d = 10, soln1)

and you will get the new list of lists $$[[x = \frac{10}{a}]]$$. If you want to see multiple substitutions, you can put them all at the start of the soln command:

subs(a=3, d = 10, soln1)

will give $$[[x = \frac{10}{3}]]$$