**source transformation**, i.e.

**voltage source to current source transformation**and

**current source to voltage source transformation**in detail.

An **energy source**
is a type of **active circuit element**
that can provide excitation to the circuit. In simple words, an **energy source** is a circuit element
that can deliver power to the circuit.

In electrical engineering, we come across two types of energy sources namely,

- Voltage sources
- Current sources

A **voltage source**
is a type of energy source that maintains a constant voltage across its
terminals whatever current may be drawn from it. Therefore, for a voltage, the
terminal voltage remains constant and it is independent of the current taken from
the source.

On the other hand, a **current
source** is one which delivers a constant current to the circuit and this
current is independent of the voltage across its terminals.

However, based on the **internal
resistance**, the voltage and current sources are further classified into the following types:

- Ideal voltage source
- Practical/real voltage source
- Ideal current source
- Practical/real voltage source

An **ideal voltage
source** is one whose internal resistance is zero, while a** practical voltage source** has an
internal resistance of finite value in series with the ideal voltage source.

An **ideal current
source** is the type of current source for which the internal resistance is
infinite, whereas a **practical current
source** has some finite resistance that is connected in parallel with an
ideal current source.

Although, a practical voltage source can be converted into a
practical current source and a practical current source can be converted into a
practical voltage source by the **source
transformation technique**. The source transformation is sometimes very
helpful in simplifying the electrical circuit during **circuit analysis**.

**Voltage Source to Current Source Transformation**

According to **source transformation
theory**, a practical or real voltage source of voltage V volts in series
with an internal resistance R_{iv} can be replaced with a current
source of current I_{s} in parallel with an internal resistance R_{ic}.

`\I_s=V/R_{iv}" and "R_{ic}=R_{iv}`

It always should be kept in mind that the direction of current of the current source should not be changed at the load terminals, i.e. the current should be leaving from the positive terminal.

**Proof:**

It can be easily proved that the above
two parameters (I_{s} and R_{ic}) are technically valid. For
this consider a transformation circuit of a voltage source into a current source (refer to the above figure).

Here, we can follow the following step to
prove the conversion of a real voltage source into a real current source:

**Step
1** – In order to find the value of I_{s}, short circuit
the load terminals (x-y) of the voltage source (refer to the left figure shown below) and calculate the short circuit current I_{vsc}
as:

`\I_{vsc}=V/R_{iv}`

**Step
2** – Short circuit the load terminals of the current source (refer to the right figure shown above) and calculate the short circuit current I_{csc} as:

`\I_{csc}=I_s`

It is because the current always follows the path of low resistance. Hence, the total source current ideally flows through the short circuit.

**Step
3** – Two sources are identical if currents at the load terminals
are the same, i.e.

`\I_{vsc}=I_{csc}`

`\⟹V/R_{iv} =I_s`

**Step
4** – Now to prove that R_{iv} = R_{ic}, open the
load terminals of both the voltage source and current source and deactivate the
sources (i.e. short-circuit the voltage source and open circuit the current
source) refer to the below figures. Then, calculate the resistance of both the
circuit viewing from the load terminals x-y.

`\R_{vxy}=R_{iv}`

And

`\R_{cxy}=R_{ic}`

**Step
5** – Again two sources are identical if their resistances viewing
from the load terminals are equal, i.e.

**Current Source to Voltage Source
Transformation**

By using the source transformation technique, we can also convert a practical current source into a practical voltage source.

According to this, a real current source with source current I and a parallel internal resistance R

_{ic}can be converted into a real voltage source of voltage V and a series internal resistance R

_{iv}, where,

`\V=IR_{ic}`

And

`\R_{iv}=R_{ic}`

This can also be proved in the same way
as the proof of voltage-to-current source transformation.

**Numerical
example** – A voltage source of 12 V having an
internal resistance of 2 ohms, it is required to transform it into an
equivalent current source. Calculate the current and internal resistance of the
equivalent current source.

**Solution**
–

For the voltage source,

`\V=12" V"`

`\R_iv=2" Î©"`

Now, the current and internal resistance
of the equivalent current source will be,

`\I_S=V/R_{iv} =12/2=6" A"`

And

`\R_{ic}=R_{iv}=2" Î©"`

Hence, I_{s} and R_{ic}
will be connected in parallel to obtain the current source equivalent to the
given voltage source.

Therefore, in this article, we have discussed everything about source transformation along with proof of statements and solved numerical examples.

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