Superposition Theorem

Superposition theorem states that” In an active linear network containing several sources(including dependent sources) , the overall response(branch current or voltage) in any branch in the network equals the algebraic sum of the responses of each individual source considered separately with all other sources made inoperative, i.e replaced by their internal resistances or impedances.”

For voltage sources to make a source inoperative it is short circuited leaving behind its internal resistance or impedance.

For current sources to make a source inoperative it is open circuited leaving behind its internal resistance or impedance.

The principle of superposition is the combined property of additivity and homogeneity.

Explanation of Superposition Theorem

Consider voltage sources V1 and V2 respectively. Applying the superposition theorem in the given circuit,

consider voltage source V1 and replace voltage source V2 by a short circuit. I’ is the current in the R3 resistance.

The current from the voltage source V1 is,

Now consider voltage source V2 and replace V1 by a short circuit. I” is the current in R3 resistance.

The current from the voltage source V2 is,

Now when we apply super position theorem, then current through resistance R3 is,

Applications of Super-position Theorem

• It is applicable for any linear circuit having time-varying or time-invariant elements.
• It is useful in circuit analysis for finding the values of current and voltage in any branch of the circuit, when the circuit has large number of independent sources.

Limitations of Super-position Theorem

• It is not applicable to the circuits containing of only dependent sources.
• It is not applicable to the circuits consisting of non-linear elements like diode, transistor etc.
• Also not applicable for calculation of power ,as the power is proportional to the square of current or voltage(non-linear).
• It is not applicable to the circuits consisting of less than two independent sources.