Chapter 7, Problem 3P

Consider the two-loop circuit shown in Fig P7.3. The currents $l_1$ and $l_2$ (in A) satisfy the following system of equations:

$1100l_1+1000l_2-9=0$ $(7.88)$ $1100l_2+1000l_1=0$ $(7.89)$

(a)Find $l_1$ and $l_2$ using the substitutions method.

(b) Write the system of equations $(7.88)$ and $(7.89)$ in the matrix form $AI=b$, where $I=\left[\begin{array}{c}{I}_1\\ I_2\end{array}\right]$.

(c) Find $l_1$ and $l_2$ using the matrix algebra method. Perform all computations by hand and show all steps.

(d) Find $l_1$ and $l_2$ using the Cramer’s rule.