Superposition Theorem


Superposition Theorem

The superposition principle states
“that the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone”.


Superposition is not limited to circuit analysis but is applicable in many fields where cause and effect bear a linear relationship to one another

Steps to Apply Superposition Principle

 1. Turn off all independent sources except one source. Find the output (voltage or current) due to that active source using the steps used in KVL & KCL.
2. Repeat step 1 for each of the other independent sources.
      3. Find the total contribution by adding algebraically all the         contributions due to the independent sources.

Let us solve one question with load resistance 4 ohm

                                                
Sol
Consider 6 v source only

Open the 3a source and apply b and apply kcl to determine current through load resistance.

Apply similar rules of kvl and kcl

After applying voltage dividing rule V1= 2V appears across load resistance. 

Similarly by applying current division rule and kcl we get V2 = 8V

And V= V1+V2

V= 10V

Comments

Post a Comment

Popular posts from this blog

Equivalent Ckt of transformer

Image
Equivalent circuit of no load transformer equivalent circuit  In the given figure we take primary referred equivalent. I 2 ’ = I 2 \a                       where,          a = turn ratio = N 1 \N 2 R 2 ’ = a 2 R 2                                    Gi = R 0        B m = X 0 X 2 ’= a 2 X 2 V 2 ’ = aV 2                     approximation circuit Full load equivalent phasor diagram for inductive load. The KVL equations for the primary and secondary circuits are V 1 = E 1 + I 1 R 1 + j I 1 X 1 V 2 = E 2 - I 2 R 2 - j I 2 X 2 ...
Read more

No load equivalent circuit

Image
No load equivalent circuit The primary winding draws a small amount of alternating current of instantaneous value I o , called the exciting current , from the voltage source. The exciting current establishes flux f in the core. When the primary side is connected to sinusoidal voltage source V 1 a current known magnetizing current I m flows in it. This current set up a alternating flux in the core. Hence it is called a magnetizing current. The flux Φ m is proportional to I m . I m lags behind the applied voltage v 1 by 90.    The flux Φ m links with both the primary and the secondary winding. When it links with primary winding it produce self induce EMF E 1 which is opposite to applied voltage. Similarly alternating flux links with secondary side its produce mutually induced EMF E 2 . Both E 1 and E 2 lag behind the Φ by 90 degree. This can be shown by the phasor diagram. Here the losses are neglected. No load equivale...
Read more

NPN transistor

Image
The most commonly used transistor configuration is the  NPN Transistor . In this, we used common emitter configuration of NPN Transistors. The transistor has three regions, namely ; emitter, base and collector. The base is much thinner than the emitter while collector is wider than both as shown. However, for the  sake of convenience, it is customary to show emitter and collector to be of equal size. The emitter is heavily doped so that it can inject a large number of charge carriers (electrons or holes) into the base.  The base is lightly doped and very thin ; it passes most of the emitter injected charge carriers to the collector. The collector is moderately doped The resistance of emitter diode (forward biased) is very small as compared to collector  diode (reverse biased).  Therefore, forward bias applied to the emitter diode is generally very small  whereas reverse bias on the collector diode is much higher.    ...
Read more