Voltage source is not different from a current source. A source may work as voltage source as well as current source. It depends on working condition. If the value of load resistance is large as compared to the source's internal resistance, source is treated as voltage source. On other hand , if load resistance is very small as compared source's internal resistance, source is treated as a current source. It is possible to convert a voltage source into a current source and vice-versa.
Equivalence Between voltages source into current source .
In order to establish equivalence between a voltage source and current source, consider an a.c. source connected to load resistance (Rl). We know that this source may be treated as voltage source or current source as shown in above figure. The voltage source representation consists of an ideal voltage source (Vs) in series with a source resistance (Rs1). The current source representation are of the same source (Is) in parallel with source resistance (Rs2).Since both these presentation are of the same source , therefore they must give the same results.
Let , the value of the load resistance (Rl) is reduced to zero.i.e. terminals A and B are short-circuited , then the current through the short-circuited load ,
IL = Vs / Rs1 .........(1)
Let, the value of load resistance (Rl) is reduced to zero.In this case, the value of current through the short circuited load is equal to the source current Is ( The total resistance of a parallel combination found by Rs2 and short circuited is equivalent to a short circuit ).
Therefore, if the voltage source representation and the current source represenatation are to be equal to Is i.e. IL = Is = Vs / Rs1 ............ (2)
Again consider above two representation of the source and RL be disconnected from the source i.e. terminals A and B are open-circuited. In the voltage-source representation , this open-circuit terminal voltage is equal to the source voltage .
VT = Vs ..........(3)
In the current-source representation , the open-circuit terminal voltage,
VT = Is. Rs2 ............ (4)
and for the two representation to be equal , we can state that ,
VT = Vs = Is.Rs2 ..........(5)
we have , Vs = Is. Rs1 ..........(6) ( from (2) )
Therefore from (6) and (5)
Is. Rs1 = Is. Rs2
i.e. Rs1 = Rs2
From above equation , we can say that two representation shows same source resistance.
Let , Rs1 = Rs2 = R
Hence , Vs = Is.Rs ..... (7)
We have established the equivalence between the voltage-source and current-source representation for RL = 0 and RL = ∞ . If we take some finite value of RL i.e. 0 < RL < ∞ ., equivalence between these two representation found to be equal.
From voltage-source representation , IL1 = Vs / ( Rs + RL )
From current-source representation , IL2 = Is * Rs / ( Rs + RL ) = Vs / (Rs + RL ) ... from (7)
IL1 = IL2 , this indicates that whatever the value of RL2 , current drawn from resistance from both voltage-source representation and current-source representation is same. This gives equivalence between a voltage-source and current-source.
Conversion of Voltage Source into Current Source :
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| Voltage source to current source conversion |
Consider voltage source Vs with internal resistance of Rs . For conversion into equivalent current source representation ,let us short-circuit the terminals A and B and then find the current through this short-circuit terminals. This is given as , Is = Vs / Rs. It is represented by current-source (Is) in parallel with a source resistance.
Conversion of Current Source into Voltage Source :
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| Current source to voltage source conversion |
Consider current source Is with internal resistance Rs. In order to convert it into its equivalent voltage-source representation.Let us find the open-circuit terminal voltage. We get , Vs = Is . Rs Since, the internal resistance of the voltage-source is the same as that of current source, therefore we get its equivalent voltage-source representation.