Problem 232 Compute the power absorbed in each element for t

Problem #2.32 Compute the power absorbed in each element for the circuit shown in Fig. P2.32.

76 CHAPTER 3. wVE cRcurrs RESIST 2.32 Compute the power absorbed in each element for the circuit shown in Fig. P2.32. 30 15 n VA 120 v ure P232

Solution

The extended geometrician rule are often wont to realize the best divisor of 2 numbers, and, if that greatest divisor is if truth be told one, it can even be wont to realize standard inverses. The result follows since, given numbers A,BA,B , the rule finds numbers x,y,gx,y,g such Ax+By=gAx+By=g , wherever gg is that the greatest divisor. the tactic involves following the numbers within the geometrician rule within the kind Ax\'+By\'Ax\'+By\' at each step. one in all the simplest ways in which to trace these numbers is as a matrix. The geometrician rule will then be viewed as a row reduction rule, subtracting whole number multiples of 1 row of the matrix from another till the ultimate column contains a zero.

For example, starting with thirty five and three, we tend to begin by writing

(1001)(353)=(353)(1001)(353)=(353)

Subtract eleven times the second row from the primary, then swap the rows:

(011-11)(353)=(32)(011-11)(353)=(32)

Subtract the second row from the primary, swap the rows:

(1-1-1112)(353)=(21)(1-11-112)(353)=(21)

Finally deduct doubly the second row from the primary, and once more swap:

(-1312-35)(353)=(10)(-1123-35)(353)=(10)