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Source Conversion

A given voltage source with a series resistance can be converted into (or replaced by) an equivalent current source with a parallel resistance.

Conversely, a current source with a parallel resistance can be converted into a voltage source with a series resistance.

Suppose, we want to convert the voltage source of Fig. 46 (i) into an equivalent current source. To do so, we shall find the value of current, supplied by the source when a ‘short’ is put across terminals L and M as shown in Fig. 46 (ii) ; this current is I = V/ A current source supplying this current I and having the same resistance R connected in parallel with it represents the equivalent source. It is shown in Fig. 46 (iii).

  • Similarly, a current source of I and a parallel resistance R can be converted into a voltage source of voltage V = IR and a resistance R in series with it.

It may be kept in mind that a voltage source-series resistance combination is equivalent to for replaceable by) a constant source-parallel resistance combination if, and only if their respective 4101m-circuit voltages are equal, and respective short-circuit currents are equal.

 

Example. Refer Fig. 46 (i ). Voltage across terminals L and M when they are open (i.e. open-circuit voltage V oc) is V itself because there is no drop across R. Short-circuit current across LM = I = V / R

Refer Fig. 46 (iii). The open circuit voltage across LM = drop across R = IR = V.

If a short is placed across LM, whole of I passes through it because R is completely shorted out

 

Example 12 . Convert the voltage source of Fig. 47 (i) into an equivalent current source.

Solution. As shown in Fig. 4 7 (ii), current obtained by putting a short across terminals L and M is 20 / 10 = 2A

Hence the equivalent current source is as shown in Fig. 47 (iii).

 

Example 13. Find the equivalent voltage source for the current source in Fig. 48 (i).

Solution. The open-circuit voltage across termainals A and Bin Fig. 48 (i ) is V oc = drop across = 2 X 5 = 10 V.

Hence, voltage source has a voltage of 10 V and the same resistance of  n connected in series [fig" 48 (ii)].