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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 73 (page 716)

An application of Kirchhoff鈥檚 Rules to the circuit shown below results in the following system of equations:
$I_{2} = I_{1} + I_{3} 5 - 3 I_{1} - 5 I_{2} = 0 10 - 5 I_{2} - 7 I_{3} = 0$
Find the values of currents

Short Answer

Expert verified

The values of current are $\frac{10}{71}, \frac{65}{71}, \frac{55}{71}$ .

Step by step solution

01

Given information

We are given a system of equation

$I_{2} = I_{1} + I_{3} 5 - 3 I_{1} - 5 I_{2} = 0 10 - 5 I_{2} - 7 I_{3} = 0$

02

Simplify the equation

Substitute the equation 1 in equation 2 and 3 we get

equation 2 becomes

$5 - 3 I_{1} - 5 (I_{1} + I_{3}) = 0 5 - 8 I_{1} - 5 I_{3} = 0 8 I_{1} + 5 I_{3} = 5 (4)$

Equation 3 becomes

$10 - 5 (I_{1} + I_{3}) = 7 I_{3} 10 - 5 I_{1} - 5 I_{3} = 7 I_{3} 5 I_{1} + 12 I_{3} = 10 (5)$

Multiply equation 4 by -5 and equation 5 by 8

And then add them

We get,

$- 40 I_{1} - 25 I_{3} = - 25 + 40 I_{1} + 96 I_{3} = 80 71 I_{3} = 55$

Therefore $I_{3} = \frac{55}{71}$

03

Find the remaining values

We get,

$8 I_{1} + 5 I_{3} = 5 8 I_{1} + 5 (\frac{55}{71}) = 5 I_{1} = \frac{10}{71}$

We also have

$I_{2} = I_{1} + I_{3} I_{2} = \frac{10}{71} + \frac{55}{71} I_{2} = \frac{65}{71}$

04

Conclusion

The values of current are $\frac{10}{71}, \frac{65}{71}, \frac{55}{71}$ .

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Most popular questions from this chapter

Running a Race : In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner?

(a) Graph the line : $3 x + 4 y = 12$ .

(b) What is the slope of a line parallel to this line?

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{matrix} 3 x = 24 \\ x + 2 y = 0 \end{matrix}$

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{matrix} x + 3 y = 5 \\ 2 x - 3 y = - 8 \end{matrix}$

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$x - 2 y + 3 z = 7 2 x + y + z = 4 - 3 x + 2 y - 2 z = - 10$

See all solutions

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