# Independent and dependent source

In this article, we discuss two types of electrical sources, known as independent and dependent sources.

An electrical source is a source that supplies energy to the network. Based on the dependence of other elements in the circuit, the electrical source is divided into two parts one is an independent source and the other is the dependent source.

## Independent source

Independent source refers to the source which can deliver energy and the output does not depend on any other elements in the circuit, i.e the magnitude of the output voltage or current will not change with any variations by elements connected in the network. An Independent source can be a voltage source or a current source.

## Dependent source

A dependent source which is also known as a controlled source refers to those sources in which the output depends on other elements present in the circuit.

It is classified into 4 categories that are listed below:

### The current dependent current source

When the output current of the source is dependent on the current flowing in the circuit, this type of source is called the current-dependent current source.

Mathematically this can be written as,

Iab = X1Icd

Where,

X1 is a constant and Icd is the current flowing in the circuit.

### Current dependent voltage source

In current dependent voltage source the output voltage of the source is dependent on the current flowing through the elements in the circuit.

Mathematically this can be expressed as,

Vab = X2Icd

Where,

X2 is a constant and Icd is the current flowing in the circuit.

### Voltage-dependent voltage source

A voltage-dependent voltage source is an electrical source in which the output voltage is dependent on the voltage across the elements in the circuit

Mathematically,

Vab = X3Vcd

Where,

X3 is a constant and Vcd is the voltage across the terminal.

### Voltage-dependent current source

The output of the voltage-dependent current source depends on the voltage across the terminal.

So,

Iab = X4Vcd

Where,

X4 is a constant and Vcd is the voltage across the terminal.