# 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 R_{L} 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 R_{L }then all the current goes through the internal resistance R_{i}. The terminal voltage between A and B is the same of internal resistance R_{i} voltage for open circuit. Voltage across the internal resistance R_{i} isV = I R_{i}. 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 R_{L} to short circuit then we get short circuit current,

I_{short} = V/ R_{i}

Similarly we get short circuit current from figure 2. If we short the path removing R_{L} load resistance current I_{short }bypasses R_{i }in favour of short circuit. This is clear indication that the current I_{short }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.

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