Example

Let's find the AC current i₂ in the circuit of Figure 64.

**Figure 64:** Example.
$\begin{figure} \begin{center} \epsfig{file=images/tximg3.eps}\end{center}\end{figure}$

The phasor circuit is shown in Figure 65.

**Figure 65:** Example, phasor circuit.
$\begin{figure} \begin{center} \epsfig{file=images/tximg4.eps}\end{center}\end{figure}$

Let's use, for illustration, the use of the impedance parameters. Replace the transformer by its impedance model to obtain the circuit of Figure 66.

**Figure 66:** Example, phasor circuit, impedenace model.
$\begin{figure} \begin{center} \epsfig{file=images/tximg5.eps}\end{center}\end{figure}$

The mesh equations are

$\begin{displaymath}\begin{array}{rl} 5\angle 0 & = (1+j\frac{7}{2}) {\mathbf I}_... ...rac{7}{4} {\mathbf I}_1 + (4 + j14) {\mathbf I}_2 . \end{array}\end{displaymath}$

Solving for I₂ we get

$\begin{displaymath}{\mathbf I}_2 = 0.792 -j 135.9 = 0.157\angle -59.8^\circ \ {\rm A}. \end{displaymath}$

Therefore

$\begin{displaymath}i_2(t) = 0.157 \cos (7t -59.8^\circ) \ {\rm A} . \end{displaymath}$

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