Plotting Total Power for R=2 Ohms - V1,V2 Range 0-20V, Va = 0

[chart2006]

For R=2 ohms plot Va as a function of V1 and V2. For V1 and V2 are between 0 and 20 volts. Second part is to find the values of V1 and V2 that produce Va = 0 while minimizing the total power absorbed by the resistors (hint you may want a second plot of total power as a function of V1 and V2).

R = 2 ohms
V1 = 0:1:20
V2 = 0:1:20
Va = in terms of V1 and V2/=0
KCL at supernode

As you can see I've already solved the first part. and here is the equations or KCL being applied at the supernode. I've also set Va equal to zero and solved getting 16 = V1 - V2. Now I'm at a loss as to how to proceed. The plotting part in Matlab is easy but I'm unsure how what the second part is even really asking. Any help would be greatly appreciated.

 

[Valkarie]

The second part is asking you to find the values of V1 and V2 that minimize the total power absorbed by the resistors. To do this, you need to calculate the total power for each combination of V1 and V2. The total power is given by the equation P = (V1^2 + V2^2)/R, where R is the resistance of the resistors. You can then create a plot of total power as a function of V1 and V2 and find the combination of V1 and V2 that minimizes the total power.

 

[Mene]

For the second part, you are essentially trying to find the combination of V1 and V2 that will result in Va = 0 while minimizing the total power absorbed by the resistors. This can be achieved by finding the minimum value of the total power function as a function of V1 and V2.

To do this, you can use the equations you have already derived for KCL at the supernode and set Va = 0. This will give you a relation between V1 and V2, which can be used to eliminate one variable in the total power function. Then, you can take the derivative of the total power function with respect to the remaining variable and set it equal to 0 to find the minimum value.

Once you have the minimum value, you can plug it back into the equation for Va and solve for the corresponding values of V1 and V2. These values will produce Va = 0 and minimize the total power absorbed by the resistors.

In terms of plotting this in Matlab, you can use the "fminsearch" function to find the minimum value of the total power function and then use the corresponding values of V1 and V2 to plot the total power function as a function of V1 and V2. This will show the minimum power value on the plot and the corresponding values of V1 and V2 that achieve it.