Chapter 11: Q. 73 (page 716)

An application of Kirchhoff’s 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

Given information

We are given a system of equation

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

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

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

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

Conclusion

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

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An application of Kirchhoff’s 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

Step by step solution

Given information

Simplify the equation

Find the remaining values

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

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An application of Kirchhoff’s Rules to the circuit shown below results in the following system of equations:I2=I1+I35-3I1-5I2=010-5I2-7I3=0Find the values of currents

Short Answer

Step by step solution

Given information

Simplify the equation

Find the remaining values

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Geometry

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

An application of Kirchhoff’s 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