Voltage source to current source conversion
Conversion of voltage source into current source is possible when a voltage source is equal to current source. Figure 1 is a circuit of constant voltage source and figure 2 is a circuit of constant current source. If the two circuits are satisfied electrically the same way under all condition then we can convert voltage source to current source having no doubt.
Condition 1: In figure 1 if the supply voltage is V and we remove the load resistance RL then it becomes open circuit. In this situation the terminal voltage between point A and B is V. In figure 2 if we remove the load resistance RL then all the current goes through the internal resistance Ri. The terminal voltage between A and B is the same of internal resistance Ri voltage for open circuit. Voltage across the internal resistance Ri isV = I Ri. As open circuit voltage between two circuits is electrically equal and that is V. So the circuits are equivalent.
Condition 2: In figure 1 if we make the load RL to short circuit then we get short circuit current,
Ishort = V/ Ri
Similarly we get short circuit current from figure 2. If we short the path removing RL load resistance current Ishort bypasses Ri in favour of short circuit. This is clear indication that the current Ishort is electrically same between two circuits.
In this way we can convert a constant voltage source to a constant current source. Following steps should be taken:
- Make short circuit between two terminals A and B as we done in figure. Find the short circuit current and let it be I.
- Measure the resistance at the terminals with load removed and sources of e.m.f s replaced by their internal resistances if any. Let the resistance is R.
- Then equivalent current source can be represented by a single current source of magnitude I in parallel with resistance R.
Let’s see a problem. By solving this you will get clear concept if any trouble.
Conversion of voltage source to current source problem
Problem: convert the constant voltage source shown in figure 3 to constant current source.
Here we get 20 V constant voltage source and 20Ω resistance. We have to follow the steps for conversion
(i) First place a short across A and B and find short circuit current I.
Short circuit current, I = 20/20 = 1 A
Equivalent current source has a magnitude of 1 A.
(ii) At AB terminal measure the resistance with load removed and 20V source replaced by its internal resistance. The voltage source has negligible resistance so that resistance at terminals AB is R = 20Ω.
(iii) The equivalent current source is a source of 1 A in parallel with a resistance of 20Ω as shown in figure 4.
If we apply ohm’s law in this circuit we get the voltage which is same in previous circuit so figure 3 and figure 4 are equivalent circuit and source conversion done properly. V = IR = 1×20 = 20V
Conversion of Current source to voltage source
Problem: convert the current source to voltage source for figure 5.
We have to do same inverse procedure.
From ohm’s law V = IR = 2 × 20 = 40V. So when we convert the current source to voltage source it will give 40V supply. Redrawing the circuit for voltage source we get as figure 6 equivalent circuit.
In this way source conversion or source transformation can be possible.