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Superposition Theorem, Ideal Constant - Voltage Source

Superposition theorem
According to superposition theorem,”In any linear network containing energy source (current or voltage source) and impedance (or resistance),then the current (or voltage ) through any circuit element is obtained by avector sum of current (or voltage ) that can flow through circuit due to individual energy sources.”
Following steps should be taken to solve the linear network with help of superposition theorem:-
Step1: Take single energy source and remove the remaining energy source leaving their internal resistance.If the energy source is voltage source then remove it by short circuit and if the energy source is current source then remove it by open circuit.
Step 2: find the current (or voltage ) due to this single energy source through particular circuit element.
Step3:Repeat the above process to find current or voltage due to all other energy sources.
Step4:Finally,find the vector sum of current or voltage through that circuit element due to all energy sources.
Let us make a simple network as below:-


Strep1:Take \(V_1\) removing \(V_2\) by short circuit

Figure - 02

Step 2:$$ I_{R_1} or I_{AB}= \frac{V_1}{R_1+R_2\shortparallel R_3}$$ $$ I_{R_2} or I_{BC}=I_{R_1} \times \frac{R_3}{R_2+R_3}\times I_{R_1}$$ $$ I_{R_3}=I_{R_1} \times\frac{ R_2}{R_2+R_3}$$

Step 3:Take \(V_2\) remaining \(V_1\) by short circuit.

Fig - 03

Here $$ I_{R_2}=\frac{V_2}{R_2+R_1\shortparallel R_3}$$ $$ I_{R_1}=I_{R_2} \times \frac{R_3}{R_1+R_2} $$ $$I_{R_3}=I_{R_2} \times\frac{R_3}{R_1+R_3}$$
Step4: Vector sum of current for required circuit element gives the results.

Ideal constant voltage source
An ideal voltage source is a two-terminal device that maintains a fixed voltage drop across its terminals.It is often used as a mathematical abstraction that simplifies the analysis of real electric circuits.If the voltage across can be specified independently of any other variable in a circuit,it is called an independent voltage source.Conversely,if the voltage across an ideal voltage source is determined by some other voltage or current in a circuit.It is called a dependent or controlled voltage source.A mathematical mode of an amplifier will include dependent voltage sources whose magnitude is governed by some fixed relation to an input signal,for example.In the analysis of faults on electrical power systems,the whole network of interconnected sources and transmission lines can be usefully replaced by an ideal (AC) voltage source and a single equivalent impedance.
The thermal resistance of an ideal voltage source is zero;it is able to supply or absorb any amount of current.The current through an ideal voltage source is completely determined by the external circuit.When connected to an open circuit:there is zero power.When connected to a load resistance,the current through the source approaches infinity as the load resistance approaches zero(a short circuit ).Thus,an ideal voltage source can supply unlimited power.
No real voltage source is ideal ;all have a non-zero effective internal resistance,and none can supply unlimited current.However,the internal resistance of a real voltage source is effectively modeled in linear circuit analysis by combining a non-zero resistance in series with an ideal voltage source( Thevenin equivalent circuit).
Ideal constant current source

 Ideal constant current source
 Ideal constant current source

A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it.A current source is the dual of a voltage source.The term,constant –current sink,is sometimes used for sources fed from a negative voltage supply.Above figure shows the schematic symbol for an ideal current source,driving a resistor load.There are two types.An independent current source (or sink) delivers a current .A dependent current source delivers a current which is proportional to some other voltage or current in the circuit.
An ideal current source is a circuit is anelement where the current through it is independent of the voltage across it. It is a mathematical model,which real device can only approach in performance .If the current through an ideal current source can be specified independently of any other in a circuit,it is called an independent current source .Conversely,if the current through an ideal current source is determined by some other voltage or current in a circuit ,it is called as dependent or controlled current source .Symbols for these sources are shown in above figure.
The internal resistance of an ideal current source is infinite.An independent current source with zero current is identical to an ideal open circuit.The voltage across an ideal current source is completely determined by the circuit it is connected to a short circuit,there is zero voltage and thus zero power delivered.When connected to a load resistance,the voltage across the source approaches infinity (an open circuit ).Thus,an ideal current source,If such a thing existed in reality,could supply unlimited power and so would represent an unlimited source of energy.
No physical current source is ideal.For example,no physical current source can operate when applied to an open circuit.There are two characteristics that define a current source in real life.One is its internal resistance and other is its compliance voltage.The compliance voltage is the maximum voltage that the current source can supply to a load.Over a given load range,it is possible for some types of real current sources to exhibit nearly infinite internal resistance.However,when the current source reaches its compliance voltage,it abruptly stops being a current source.
In circuit analysis,a current source having finite internal resistance is modeled by placing the value of that resistance across an ideal current source (the Norton equivalent circuit ).However,this model is only useful when a current is operating within its compliance voltage.

Comparison between voltage and current sources
Most source of electric energy (the mains,a battery )are modeled as voltage sources.An ideal voltage sources provides no energy when it is loaded by an open circuit ( i.e. an infinite impedance ),but approaches zero (a short circuit ).Such a theoretical device would have a zero ohm output impedance in series with the sources has a very low, but non-zero internal resistance impedance: often much less than 1 ohm.
Conversely,a current source provides a constant current ,as long as the load connected to the source terminals has sufficiently low impedance.An ideal current source would provide no energy to a short circuit and approaches infinity (an open circuit ).An ideal current source has an infinite output impedance in parallel with the source.A real-world current source has a very high,but finite output impedance.In this case of transition current sources ,animpedance of a few megohms (at low frequency) is typical.




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