Superposition Theorem
Superposition theorem is quite useful for analysing electric circuits which contains 2 or more active sources. In such cases, the theorem considers each source separately to evaluate the current through or voltage across a component. The resultant is given by sum of all the currents or voltages caused by each source acting independently. Superposition theorem can be stated as follows
"The current through or voltage across element in the linear circuit containing a number of sources is the algebraic sum of currents or voltages because of each source acting alone, all other sources being removed at that time."
Linearity is a essential condition for theorem to apply. Fortunately, v, i relationship for R, L and C are all linear in nature.
The sources can be removed by using following steps,
1. Ideal voltage sources are short-circuited
2. Ideal current sources are open-circuited
Generally, practical sources are replaced by the internal resistances.
Example
Find voltage VL using Superposition theorem in circuit diagram of the Figure.
Figure--An electric circuit containing multiple sources.
Step 1: Suppressing 1 A current source by replacing it with the open circuit
This will result in circuit diagram of Figure (a). The output voltage, now called V'L is the 5Ω voltage across the resistance. As both 10Ω and 5Ω are in series, VDR isapplied here
Figure--Application of superposition theorem to Figure
Step 2: Suppressing 10 V voltage source by replacing it with the short circuit
The resulting circuit diagram is shown in the Figure(b). The output voltage is represented by V''Land has same polarity as VL. It is obvious that both resistors are in parallel and thus CDR can be applied to determine current flowing through resistor.
The total voltage, according to superposition theorem is given by the sum of V'L and V''Lthat is
Superposition Theorem - Power Calculation
Although superposition theorem can be used to find out the voltage across and current through a circuit element by adding the responses due to each source acting alone, the power (as a nonlinear relationship) cannot be evaluated until net voltage or current is found. Because
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