Table 3.1 Scheme Parametres

Number of the Variant	В	В	В	В	В	В	Ом	Ом	Ом	Ом	Ом	Ом
1-6	130	500	120	240	170	380	21	14	13	16	9	20
7-12	360	190	210	130	450	170	8	9	16	13	21	12
13-18	120	220	340	80	510	160	5	18	12	14	7	28
19-24	280	540	310	160	90	360	12	6	24	10	14	18
25-31	340	110	280	210	130	260	27	30	4	6	22	11

P=a_ik /a_kk

Figure 3.1 – Gaussian Method Forward Trace

Figure 3.2 – Gaussian Method Return Trace

Figure 3.3 – Schemes for the Task 3.2

Laboratory Work 4 solution of the linear equation systems with the complex coefficients

Purpose of the work: to learn to compute static modes in the branched electric circuits.

4.1 Theoretical Data

If there are resistor, dc sources, resistance coils, capacitors and ac sources in the electric circuit, to compute current and tension in constant modes the equation systems with the complex coefficients are solved. If the element static characteristic nonlinearity is not taken into account, the algebraic equation linear system is obtained. To solve it all methods mentioned in the previous laboratory work, including the Gaussian method, are applied.

The specificity of the solution is in fact that we operate with the complex numbers rather than with real ones. Such algorithmic languages as FORTRAN and PL-1 have the complex type data and operate with it as easily as with the real type arithmetic data.

When the Pascal language is used the programmer has to make up the sub-programme to do the operations with the complex numbers. It can be done much easier due to the possibility to create the types identified by the user, and the presence of the formal and actual parameter device in the sub-programmes. For example, in the Pascal programme description part the data complex type can be defined as the record which consists of two parts: real (re) and imaginary

type complex = record

re, іm: real

end;

Then a number of sub-programmes and functions to work with the complex numbers are made up. For example, the sub-programme of multiplication of two complex numbers X=X +jX і Y=Y +jY can be as follows:

procedure MultС(x,y:complex; var z:complex);

begіn

z.re:=x.re*y.re-x.іm*y.іm;

z.іm:=x.re*y.іm+x.іm*y.re;

end;