Superposition Theorem

Superposition Theorem to simplify electric networks

The superposition Theorem is used to analyze networks with multiple energy sources (current or voltage sources).

In principle, it involves considering the effect in terms of current or voltage of the individual current or voltage sources on their own and combining them at the end. 

Example - Simplifying according to the superposition theorem

The following circuit is given (figure a) with a voltage source and a current source. Your task: Calculate the individual currents of this circuit

Superposition Theorem – DC Network Analysis - Explanation, Solved Examples

Example - Simplifying according to the superposition theorem
The following circuit is given (figure a) with a voltage source and a current source. Your task: Calculate the individual currents of this circuit.

Step 1: Viewing the voltage source on the left - current source on the right is "removed"

Figure b shows the following:

I₁₁ = I₃₁ = V_S / R₂ + R₂ + R₃ = 12 V / 60 Ω = 0,2 A

Step 2: Viewing the current source on the right - voltage source on the left is removed

Figure C shows the following:

I₃₂ = I_q * R₁₂₃ / R₃ = 5A * 15 Ω / 30 Ω = 2,5A  Current divider rule

I_q + I₁₂ - I₃₂ = 0    Junction rule

⇒ I₁₂ = I₃₂ - I_q = 2,5A - 5A = - 2,5A

Additional calculation:  R₁₂ = R₁ + R₂ = 30 Ω;   R₁₂₃ = R₁₂ II R₃ = 15Ω

Step 3: Add up the individual effects of the sources

I₁ = I₁₁ + I₁₂ = 0,2A - 2,5A = -2,3A

I₃ = I₃₁ + I₃₂ = 0,2A + 2,5A = 2,7A

Note: Because the current arrow of I₁ points to the node, the value of I₁ is negative.