## Superposition Theorem with example

**SUPERPOSITION THEOREM**

This theorem finds use in solving a network where two or more sources are present and connected not in series or in parallel.

**Statement of superposition theorem**

If a number of voltage or current sources are acting simultaneously in a linear network,the resultant current in any branch is the algebraic sum of the currents that would be produced in it,when each source acts alone replacing all other independent sources by their internal resistances.

Steps for solving a network using the Principle of superposition

Step1: take only one independent source of voltage/current and deactivate the other independent voltage/current sources.(For voltage sources,remove the source and short circuit the respective circuit terminals and for current sources,just delete the sources keeping the respective circuit terminal open).Obtain branch currents.

Step2: Repeat the above step for each of the independent sources.

Step3: To determine the net branch current utilizing superposition theorem,just add the currents obtained in step 1 and step 2 for each branch.If the currents obtained in step 1 and step 2 are in the same direction just add them;on the other hand,if the respective currents are directed opposite in each step,assume the direction of the clockwise current to be positive and subtract the current obtained in the next step from the original current.The net current in each branch is the obtained.

Example:

fig1

In this figure when Vo=0,I=2A; Find I when Vo=10V

Solution:When Vo=0,the circuit will look like fig2

Here I=2A.

Next when Vo=10V is applied

Utilising the concept of superposition, the circuit diagram is

for the voltage source alone.This time I=10/(2+2)=2.5A

Thus,net current through the require d resister I=2+2.5=4.5A as per superposition theorem.

The Superposition Theorem finds use in the study of alternating current (AC) circuits, and semiconductor (amplifier) circuits, where sometimes AC is often mixed (superimposed) with DC. Because AC voltage and current equations (Ohm’s Law) are linear just like DC, we can use Superposition to analyze the circuit with just the DC power source, then just the AC power source, combining the results to tell what will happen with both AC and DC sources in effect. For now, though, Superposition will suffice as a break from having to do simultaneous equations to analyze a circuit.

**Preview: The Superposition Theorem states that a circuit can be analyzed with only one source of power at a time, the corresponding component voltages and currents algebraically added to find out what they’ll do with all power sources in effect. To negate all but one power source for analysis, replace any source of voltage (batteries) with a wire; replace any current source with an open (break).**

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