Penes

Exercise 1
the arrays are increasingly growing number of applications in the solution
problems in science and technology.
Apply here the calculation of currents in a "grid". Treatment willspecial recalculation of the intensities of the currents in each "loop" of the network when
amending the electromotive forces of the sources due to failures or changes in
thereof.
To illustratethis from an example:
The following diagram shows a simple model of an electrical network consisting of
batteries, cables and resistors.

From Kirchoff's laws which state that the sum ofthe electromotive forces
sources (batteries or other power generators) in each "loop" of the network is equal to
sum of the products IR (intensity x resistance), we arrive to the system of equations
simultaneous linear:The system of equations in matrix form is: RI = V (Matrix expression for the law
Ohm), wherein:

The rows of the matrix R derived from the sums of the resistances in the loop i, which
arethe diagonal elements iir, the other elements of the row, r i j ij, ≠ correspond to the common resistance to the branch line between loops i, j, i ≠ j with negative.
The problem that arises is torecalculate the column vector I, from changes in the
column vector of electromotive force (voltage) V, due to defects in source or Other changes possibly unexpected. One way that I look natural is torecalculate from the equation R = R-1
V, since the
matrix R is not always unique method is considered undesirable for reasons
cited in the study.
Will consider the appropriateness of usingthe LU decomposition in place.

Exercise 2
 Va = Vb Taking = 12V, R1 = 1Ω, R2 = R3 = 2Ω and 3Ω,
determine voltages and currents in the circuit under consideration. Interpret results.
i1 i2
We will now show away
to systematize and simplify deduction
of the equations of a circuit through
Introduction-of other variables,
mesh current calls. We consider two currents i1 and i2 as illustrated in...