Chapter 7, Problem 33P

Consider the two-loop circuit shown in Fig. P7.33. The currents $I_1$ and $I_2$ (in A) satisfy the following system of equations:

$\left(0.2s+10\right)I_1-0.2I_2=\frac{100}{s}$ $(7.140)$ $-0.2s{I}_1+\left(0.2s+\frac{10}{s}\right)I_2=0$. $(7.141)$

(a) Find $I_1$ and $I_2$ using the substitution method.

(b) Write the system of equations $(7.140)$ and $(7.141)$ in the matrix form $AI=b$, where $I=\left[\frac{I_1}{I_2}\right]$.

(c) Find $I_1$ and $I_2$ using the matrix algebra method.

(d) Find $I_1$ and $I_2$ using the Cramer’s rule.