**Superposition Theorem**

This theorem is useful for those circuits that contain two or more than two sources. This theorem is applicable only when network or circuit contains with linear elements. The sources of emf connected only in parallel not in series. According to this theorem the current flowing through any section is the algebraic sum of all the currents which should flow in that section when each source of emf acts alone and all other sources are replaced by their internal resistances. In this article we will solve this theorem step by step and applications of superposition theorem.

**Explanation of superposition theorem step by step**

Consider a circuit which contains two emf source V_{1} and V_{2} and resistive elements R_{1}, R_{2} and R_{3}. You can see in figure 1.

**Step 1**

Take only one source V_{1} and replace the other source V_{2} by its internal resistance. If internal resistance is not given then it is taken as zero.

Note- If the circuit contains current source, we will delete the source from the circuit. In other words, we can say that the branch that contains current source which acts as a open circuit.

Arrow shows the direction of flow of current. Now determine the flow flowing through in various section of the circuit. The current is denoted by I_{1, }I_{2 } and I_{3}.

**Step 2.**

Now take other emf’s source V_{2} and replace the source V_{1} resistance. Determine the current flowing in various section of the circuit. The current is denoted b I_{1}” , I_{2}” and I_{3}”.

To determine the resultant current just odd the currents obtained in steps 1 and step 2. If the current obtained in step 1 and step 2 in same direction just add, on the other hand if the currents flowing through the circuit in opposite direction the it subtract them. In above explanation, currents flowing through resistance R_{1} and R_{2} is in opposite direction and in this case currents obtained by step 1 and step 2 are subtracted where as current flowing through resistance R_{3} is added.

As per superposition theorem

I_{1} = I_{1}’ – I_{1}”

I_{2} = I_{2}’ – I_{2}”

I_{3} = I_{3}’ + I_{3}”

**Applications of superposition theorem**

This theorem is applied for those circuits or networks that contains two or more than two current or voltage sources.

Limitations of Superposition Theorem

This theorem is applicable only for circuits or networks that contains only linear elements.