Independent and Dependent Current and Voltage Sources

The current and voltage sources represented during circuit analysis are either independent or dependent. The independent sources are those whose output does not depend on the current or voltage of any other branch of the network. The most well-known example of an independent source is a battery.

Battery
Battery

The emf of a battery is fixed and it depends on the chemical property of the battery, not on the current or voltage of any other branch of the network. The dc generator and alternator are also very well known examples of independent source.

Now we will think about an amplifier. The output of an amplifier is not independent, it depends on either input voltage or input current of the amplifier coming from another branch of the network. So the amplifier is an example of a dependent source. An electric source may be a current source or a voltage source. According to the dependency, dependent voltage and current sources can be categorised in four types.

Voltage Dependent Voltage Source

Here the output voltage of the source depends on the voltage of one other branch of the network.

Voltage Controlled Voltage Source
Voltage Controlled Voltage Source

Current Dependent Voltage Source

Here the output voltage of the source depends on the current of one other branch of the network.

Current Controlled Voltage Source
Current Controlled Voltage Source

Voltage Dependent Current Source

Here the output current of the source depends on the voltage of one other branch of the network.

Voltage Controlled Current Source
Voltage Controlled Current Source

Current Dependent Current Source

Here the output current of the source depends on the current of one other branch of the network.

Current Controlled Current Source
Current Controlled Current Source

The relation between the quantity on which the output depends and the output quantity is linear. The constant of this relationship is nothing but the amplification factor of the source.

The symbol of an independent source is generally represented by a circle. Often it may be represented by the symbol of a battery if the source is a battery.

Symbol of Electrical Sources
Symbol of Independent Electrical Sources

The symbol of the dependent source is generally represented by four edged diamond shape.

Both independent and dependent current and voltage sources can be time-variant or time invariant.

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