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Which is certainly not true. Also, in many of the cases that we shall consider, the voltage may not be expressible in such a simple fashion for all t, the analytic expression for v(t) depending upon the particular interval of the axis on which the point t falls. In such a case the definite integral is certainly preferable. Some such waveshapes are shown in Fig. 9. Fig. 9. Voltage waveshapes. Another important result becomes apparent if we again consider Eqs. (9). So long as the current is a continuous, differentiable function, the voltage will remain bounded.

11a), still assuming the sign before the second term to be negative, Sec. 3] Network Elements 19 corresponding to a reversal of the reference of i in Fig. 11. Let us integrate this equation from 0 to t. We will get 2 (18) We have still not used the perfect transformer condition of Eq. (14). If we do so, and rearrange terms, we will get (19) This equation is to be compared with the first one in Eqs. (15). Two differences are noted: first the appearance of the initial values of the currents, and second, the appearance of the term involving a voltage.

2 Node Equations Let us return now to a consideration of the Kirchhoff voltage law equations. We found that there are N — (N — 1) independent equa­ tions in the N branch variables. If we assign values to a suitable set of N — [N — (N — 1)] = N — 1 of the variables, the remaining ones can be expressed uniquely in terms of these. We recognize N — 1 to be the number of independent K C L equations. But these equations themselves involve N branch current variables. If it were possible to express these N current variables in terms of N — 1 voltage variables, then there would be the same number of equations as unknowns.

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