Final value theorem

FINAL VALUE THEOREM

Statement:

If f(t) and its derivative f'(t) are Laplace transformable, then the final value f(oo) of the function f(t) is given by

Table 4

To find Z(s) and Y(s) for R, L and C.

ENERGY SOURCES

Sources of electrical energy are active elements. These are classified into two types. They are (i) Voltage source and (ii) Current source.

In each of the above two, there are again two types namely ideal and non-ideal (Practical)

1.Voltage sources: A practical voltage source consists of internal resistance (source resistance) R_s in series with the source voltage V_S. The terminal voltage V_t across the load changes with change in the load current. It is due to the voltage drop across R_S.

V_t = V_s - I_s R_s

As I increases, V_t decreases. This relation between I_s and V_t is shown graphically as below.

Ideal Voltage Source:

Here the terminal voltage V_t is independent of current. It is possible only when R_S= 0. Hence the internal resistance of an ideal voltage source is Zero. The symbol for such a source and the terminal voltage - current relations of such cases are shown below.

hobi ne to VS = Vt bioto-nago el

2. Current source: A practical current source consists of resistance is parallel with the source.

I_l = I_S-I

= I_S - V/R

As V increases, I_l decreases. This V-i relation is shown in the figure below.

For an ideal current source, load current I_l is independent of V. It is possible only when R = ∞, i.e., R is open-circuited. The voltage current relation for an ideal current source is shown below.