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Our analysis in Example 1 from "Linear Algebra: Circuit Analysis" and Problem 1 from "Linear Algebra: Circuit Analysis" indicates that not enough current will flow through the lamp to make it glow. We now wish to change the resistance of the 100 ohm resistor to a new value so that the lamp will glow. We replace 100 in the equations with an unknown resistance R . Equation 2 is unchanged, but Equation 6 becomes

( v 2 - v 1 ) 50 + v 2 300 + ( v 2 - v 3 ) R = 0 6 R ( v 2 - v 1 ) + R v 2 + 300 ( v 2 - v 3 ) = 0 - 6 R v 1 + ( 7 R + 300 ) v 2 - 300 v 3 = 0 .

Equation 7 from "Linear Algebra: Circuit Analysis" becomes

( v 3 - v 2 ) R + v 3 2 = 0 2 ( v 3 - v 2 ) + R v 3 = 0 0 v 1 - 2 v 2 + ( R + 2 ) v 3 = 0 .

The matrix form of these equations is

1 0 0 - 6 R 7 R + 300 - 300 0 - 2 R + 2 v 1 v 2 v 3 = 5 0 0 .

Write a MATLAB function file calledto accept R as an input and return the matrix A in Equation 3 as an output. The first line of your function file should be builda

Now choose several values for R . For each choice, use your function b u i l d a and solve the resulting matrix equation A v = b for the voltages. Each time you choose a different R to build a different matrix A , check the determinant of A to be sure the equations have a unique solution:

Make a table of R and the corresponding values of v 3 :

Figure one is an empty table, with the leftmost column titled R, the middle column titled v_3, and a rightmost column left unlabeled. Figure one is an empty table, with the leftmost column titled R, the middle column titled v_3, and a rightmost column left unlabeled.

Now add a column to your table for the current through the lamp i = v 3 / 2 . Add rows to your table until you have found a value of R for which the lamp will glow. ( i needs to be between 0.05 and 0.075 ampere.)

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Source:  OpenStax, A first course in electrical and computer engineering. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10685/1.2
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