Source conversion formulas

The source conversion formulas are used to replace a current source to a voltage source and a voltage source to a current source.

The ideal voltage source always possesses some series resistance. This series resistance depends on the type of source and it can either be very small or very large. The figure below displays a voltage source V with an internal resistance Rs.

practical-voltage-source-symbol

Just like a voltage source, a series source always posses some internal resistance. However, the resistance of current source is in parallel:

practical-current-source-circuit

Using the source conversion formulas we can convert between the source:

source transformation formulas

Equations:

  • Formula to convert a voltage source to current source: I = V/Rs
  • Formula to convert a current source to voltage source: I = V/Rs

Let’s solve some examples to better understand this.

Example 1: A 5 V source has an internal resistance of 10 Ω. Find the equivalent current source.

Solution: I = V/Rs = 5 V/10 Ω = 0.5 A

The 0.5 amps source has a parallel resistance of 10 ohms.

Example 2: A 10 A source has an internal resistance of 18 Ω. Find the equivalent potential source.

Solution: V = IRs = 10 A * 18 Ω = 180 V.

Example 3: A 5 V source having Rs = 20 Ω is connected to a 1 kΩ resistor. Find the equivalent current source and prove that equivalent current source maintains same current and voltage in the circuit.

Solution:

source-transformation-example-3

V & I in case of V source

Potential: The voltage sources provides a 4.99 V potential to the load. You can use a voltage divider calculator or voltage division formulas to calculate the voltage in series circuits.

Here Vload = [10 kΩ/{20 Ω+ 10 kΩ}] * 5 V = 4.99 V

Current: The voltage source provides a current I = V/R = 499 µA.

Related formulas:

V & I in case of I source

Potential: The 0.25 A source provides 499 µA current.

From current divider rule: Iload = [Rs/{Rload + Rs}] * 0.25 A = 499 µA

Voltage: From Ohm’s law: V = IR = 499 µA * 10 kohm = 4.99 V

Since voltage and current remains same in  both cases this proves that source conversion is a valid rule which provides equivalent parameters.

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