# Electric circuit- dependent and independent sources

**Electric circuit**: An electric circuit is a closed path comprising of electrons flowing along it from a voltage source or a current source.

**Important points: **

1.**Source-**The point where the electrons enter an electrical circuit.

2.**Return-** exit point.

3.**Load-** The part of an electrical circuit that is between the electrons’ starting point and the point where they return to the source.

4. The electric circuit use alternating current sources.

Sources are of two types- dependent sources and independent sources

1)**Dependent source **: A dependent source is one whose value depends on some other variable in the circuit. The voltage or current values is proportional to some other voltage or current in the circuit. for example, in modelling the behavior of amplifiers.

*Examples:*

1)A bipolar junction transistor can be a dependent current source whose magnitude depends on the magnitude of the current fed into its controlling base terminal.

2)An operational amplifier can be described as a voltage source dependent on the differential input voltage between its input terminals.

*Classification:*

Dependent sources can be classified as follows:

*Voltage-controlled voltage source:* The source delivers the voltage as per the voltage of the dependent element. V=avx

*Voltage-controlled current source:* The source delivers the current as per the voltage of the dependent element. I=bvx

*Current-controlled current source:* The source delivers the current as per the current of the dependent element. I=cix

*Current-controlled voltage source:* The source delivers the voltage as per the current of the dependent element. V=Idx

-The proportionality constant between dependent and independent variables is dimensionless if they are both currents (or both voltages).

– A voltage controlled by a current has a proportionality factor expressed in units of resistance (ohm), and this constant is sometimes called “trans-resistance”.

– A current controlled by a voltage has the units of conductance , and is called “trans-conductance”.

-Trans-conductance is a commonly used specification for measuring the performance of field effect transistors and vacuum tubes.

2) **Independent sources:** Ideal Independent Source maintains same voltage or current regardless of the other elements present in the circuit.Its value is either constant (DC) or sinusoidal (AC). The strength of voltage or current is not changed by any variation in connected network.

Example: a Copper resistance along the circuit

*Classification:*

1) *Ideal Independent Voltage Sources*

An ideal independent voltage source is a two-terminal circuit element where the voltage across it

a) is independent of the current through it

b) can be specified independently of any other variable in a circuit.

In a circuit, voltage across elements which are parallel with voltage sources are equal to the voltage of the corresponding voltage sources

2) *Ideal Independent Current Sources*

In contrast to ideal independent voltage sources, an ideal independent current source is a two-terminal circuit element where the current passing through it

a) is independent of the voltage across it

b) can be specified independently of any other variable in a circuit.

**IMPORTANT QUESTION and ANSWERS**

**1)** What is an electric circuit?

**ans)** An electric circuit is a closed path comprising of electrons flowing along it from a voltage source or a current source

**2)** What are the two type of sources?

**ans)** independent and dependent sources.

**3)** What is a load?

**ans)**The part of an electrical circuit that is between the electrons’ starting point and the point where they return to the source.

**4)** What is a dependent source?

**ans)** A dependent source is one whose value depends on some other variable in the circuit.

**5)** What is the difference between dependent and independent sources?

**ans)** Dependent sources are current or voltage sources whose output value is based on time or another value from the circuit. A dependent source may be based on the voltage over a resistor for example, or even the current flowing through a given wire but Independent sources produce current/voltage at a particular rate that is dependent only on time. These sources may output a constant current/voltage, or they may output current/voltage that varies with time.

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Dependent and independent voltage

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Really informative article in simple language, really easy to comprehend. 🙂

it gives the idea about dependent and independent sources of electric circuit .properly described interested people can go through this.

Independent voltage sources are independent of the current passing through it, irrespective of its elements. This article is really understandable regarding the dependency and independency of sources.