Circuit Fundamentals

# Superposition principle

In the linear circuit with voltage sources, mesh currents are linear functions of mesh EMFs.

${I}_{i}=\frac{1}{{∆}_{R}}\sum _{k=1}^{n}{V}_{k}{∆}_{ki}$

The current in any mesh, containing more then one EMF, is an algebraic sum of mesh currents, caused by each EMF acting alone. This rule is called superposition principle. The idea of the principle is to determine the mesh current caused by each EMF in the mesh acting alone, and to sum them up.

The physical meaning of this principle states that nodal voltage of any node in linear electric circuit is an algebraic sum of the voltages that has been produced by each current source, acting alone.

Let us model a circuit with independent and dependent sources in it. Each independent source is active in only one measurement. An inactive voltage source are present like a short circuit. All inactive current sources are presented like opened circuits. Dependent sources are always active.

Superposition principle also has its limitations:

1. It works with linear circuits only.
2. It will not work with power sources.

Linear circuits contain only linear elements. Linear elements are those whose voltage-current characteristics is linear. For now we have considered only resistive linear circuits with voltage-current characteristics $v\left(t\right)=R*i\left(t\right)$. Linear dependent sources (voltage or current) are those whose variable is proportional to the first power of current or voltage, or sum of these variables. Thus linear circuits contain only linear dependent sources, linear elements and independent sources, and its response is proportional to the independent source. Further there will also be inductance and capacitance that is determined in terms of linearity.

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