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Consider the two-loop circuit shown in Fig P7.1. The currents
(a) Find
(b) Write the system of equations
(c) Find
(d) Find
![Check Mark](/static/check-mark.png)
(a)
The value of
Answer to Problem 1P
The value of
Explanation of Solution
Given:
The first system equation is:
The second system equation is:
Calculation:
Solve the system equation (1) for
Simplify further.
Substitute
Rearrange for
Substitute
Conclusion:
Thus, the value of
![Check Mark](/static/check-mark.png)
(b)
The system of equation in the form of
Answer to Problem 1P
The matrix form of the equation is
Explanation of Solution
Concept used:
The system of two simultaneous equations of variables in the form
Here,
Calculation:
The system of equations represented by equation (1) and equation (2) can be written in the matrix form as follows:
Conclusion:
Thus, the matrix form of the equation is
![Check Mark](/static/check-mark.png)
(c)
The value of
Answer to Problem 1P
The value of
Explanation of Solution
Concept used:
Write the expression to calculate the value of the current using matrix method.
Here,
Write the inverse of the matrix.
Here,
Calculation:
The equation in the form
The determinant of matrix
The adjoint of matrix
Substitute
Substitute
Conclusion:
Thus, the value of
![Check Mark](/static/check-mark.png)
(d)
The value of
Answer to Problem 1P
The value of
Explanation of Solution
Concept used:
Write the expression for
Here,
Write the expression for
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, the value of
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