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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. 74 (page 716)

An application of Kirchhoff鈥檚 Rules to the circuit shown results in the following system of equations:
$I_{3} = I_{1} + I_{2} 8 = 4 I_{3} + 6 I_{2} 8 I_{1} = 4 + 6 I_{2}$
Find the currents

Short Answer

Expert verified

The values of current are $\frac{11}{13}, \frac{6}{13}, \frac{17}{13}$ respectively.

Step by step solution

01

Given information

We are given a system of equation

$I_{3} = I_{1} + I_{2} 8 = 4 I_{3} + 6 I_{2} 8 I_{1} = 4 + 6 I_{2}$

02

Simplify the equations

Substitute equation 1 in equation 2 we get

Equation 2 becomes

$4 (I_{1} + I_{2}) + 6 I_{2} = 8 4 I_{1} + 10 I_{2} = 8 (4)$

Now we multiply equation 4 by -2 and add it to equation 3

We get,

$- 8 I_{1} - 20 I_{2} = - 16 + 8 I_{1} - 6 I_{2} = 4 - 26 I_{2} = - 12$

hence $I_{2} = \frac{12}{26}$

Now we find the remaining values

$4 I_{1} + 10 I_{2} = 8 4 I_{1} + 10 路 \frac{6}{13} = 8 I_{1} = \frac{11}{13}$

Now also,

$I_{3} = I_{1} + I_{2} I_{3} = \frac{11}{13} + \frac{6}{13} I_{3} = \frac{17}{13}$

03

Conclusion

The values of current are $\frac{11}{13}, \frac{6}{13}, \frac{17}{13}$ respectively

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Most popular questions from this chapter

In Problems 35鈥�42, graph each system of inequalities by hand.

$\{\begin{cases} x^{2} + y^{2} 鈮� 9 \\ x + y 鈮� 3 \end{cases}$

Constructing a Cylindrical Tube: A rectangular piece of cardboard, whose area is 216 square centimeters, is made into a cylindrical tube by joining together two sides of the rectangle. See the figure. If the tube is to have a volume of 224 cubic centimeters, what size cardboard should you start with?

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

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

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

$y = x - 1; y = x^{2} - 6 x + 9$

Verify that the values of the variables listed are solutions of the system of equations.

$\{\begin{matrix} 3 x + 2 y = 2 \\ x - 7 y = - 30 \end{matrix} x = - 2, y = 4; (- 2, 4)$

See all solutions

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