# Triangular Factorization : Kirchoff's Voltage Law

4. Kirchhoff's voltage law says that the sum of the voltage drops around any closed path in the network in a given direction is zero. When this principle is applied to the circuit shown in Figure 3.5, we obtain the following linear system of equations:

(R1+R3+R4)I1+ R3I2+ R4I3=E1

(1) R311 + (R2 + R3 + R5)12 ? R513 =

R411 ? R512 + (R4 + R5 + R6)13 = 0.

Use Program 3.3 to solve for the current 11, '2, and 13 if

(a) R1=1,R2=1,R3=2,R4=1,R5=2,R6=4,andE1=23,E2=29

(b) I?i = 1, R, = 0.75, R3 = 1, R4 = 2, R5 = 1, R6 = 4, and E1 = 12,

E2 = 21.5

(c) R1 = 1, R2 = 2, I?3 = 4. R4 3, R = 1, R6 = 5, and E1 = 41, E2 = 38

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following are the solutions of I1 , I2 and I3 using the program ...

#### Solution Summary

Kirchoff's Voltage Law is investigated. The principle applied to a circuit is determined.