Question

(b) Also indicate on that drawing a sufficient set of surfaces (minimal number) on which the KCL equations should be written. They may correspond to nodes or to supernodes. (c) Write the KVL and KCL equations corresponding to your selections in parts (a) and (b). These should be written in terms of the indicated currents only, by incorporating Ohm's law when appropriate. (d) Solve your equations, using MATLAB, to express the current 11(t) in terms of the two source waveforms v, (t) and is (t). i2(t) 22 14(1) i, (t) 192 tSiž42 Fig. P2-26. Circuit for Problem P2-26.

Answer 1

(a)  The required drawing is shown in figure below-

Vs(t)

KVL equations should be written over both of the two indicated paths.

(b) The required drawing is shown in figure below-

Vs(t)

KCL equations should be written at two of the indicated surfaces.

(c) The KVL and KCL equations are-

KCL l : i₁(t) + i₂(t) + i₃(t) = i_s(t)  

KCL r : 5 i₁(t) + i₂(t) + i₃(t) - i₄(t) = 0

KVL t : -2i₂(t) + 3i₃(t) = v_s(t)

KVL b : -i₁(t) + 2i₂(t) + 4i₄(t) = 0

(d) To use MATLAB, we first write these equations in matrix-vector form as-

$\begin{bmatrix} 1 & 1 & 1 & 0\\ 5&1 &1 & -1\\ 0& -2 & 3 & 0\\ -1& 2 & 0 & 4 \end{bmatrix} \begin{bmatrix} i_1{(t)}\\ i_2{(t)}\\ i_3{(t)}\\ i_4{(t)} \end{bmatrix} = \begin{bmatrix} 0\\ 0\\ 1\\ 0 \end{bmatrix}v _s{(t)} + \begin{bmatrix} 1\\ 0\\ 0\\ 0 \end{bmatrix}i _s{(t)}$

Solving these gives-

i₁(t) = 0.0290 v_s(t) - 0.3768 i_s(t)