Electricity By using Kirchhoff’s Laws, it can be shown that the currents I1, I2, and I3 that pass through the three branches of the circuit in the figure satisfy the given linear system. Solve the system to find I1, I2, and I3.
The amount of current passes through three different circuits.
Answer to Problem 46E
The value of current
Explanation of Solution
Given:
The currents
Calculation:
Let the current
Thus, rewrite the system of equations in the terms of x, y and z, and rearrange it to get the complete solution of system
The equation (1) is
The equation (2) is
The equation (3) is
To get the complete solution of system transform it into triangular system.
Multiply equation (1) by
That is,
And Add equation (3) and (4) to eliminate terms x from equation (3) as the coefficients of x-terms in both equations are negative of each other,
That is,
Multiply equation (2) by 3,
That is,
And add equation (5) and (6) to eliminate terms y from equation (3) as the coefficients of y-terms in both equations are negative of each other,
That is,
The equation (7) is new equation (3) for triangular system.
The triangular system is,
Calculate the value of z from new equation (3) of triangular system,
Substitute 0.68 for z into equation (2) to get the value of y,
Substitute 0.29 for y and 0.68 for z into equation (1) to get the value of x,
The value of x is 0.39, y is 0.29 and z is 0.68.
Therefore, the value of current
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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