Find the voltage across 2Ω resistor in the circuit shown below using Superposition theorem.

1. Break Down the Problem

To find the voltage across the 2Ω resistor using the Superposition theorem, we need to consider each independent source in the circuit one at a time, while turning off all other independent sources. This includes replacing voltage sources with short circuits and current sources with open circuits.

2. Relevant Concepts

The Superposition theorem states that in a linear circuit with multiple independent sources, the total current or voltage in any part of the circuit can be found by summing the contributions from each independent source individually.

3. Analysis and Detail

Assuming we have a circuit with a voltage source $V_1$ and a current source $I_2$, we follow the steps:

1. Consider Voltage Source $V_1$ Alone:

   • Replace the current source $I_2$ with an open circuit.
   • Analyze the circuit to find the voltage across the 2Ω resistor.

2. Consider Current Source $I_2$ Alone:

   • Replace the voltage source $V_1$ with a short circuit.
   • Analyze the circuit again to find the voltage across the 2Ω resistor.

3. Sum the Contributions:

   • Add the voltages from both scenarios to find the total voltage across the 2Ω resistor.

4. Verify and Summarize

1. Calculate the voltage from $V_1$ and denote it as $V_{R1}$.
2. Calculate the voltage from $I_2$ and denote it as $V_{R2}$.
3. The total voltage across the 2Ω resistor is given by: $V_{total} = V_{R1} + V_{R2}$
4. Ensure calculations are correct, and summarize the results.

Final Answer

The final voltage across the 2Ω resistor is $V_{total}$.