1. **Problem Statement:** Calculate the voltage drop across the 2 ohm resistor using the superposition theorem. 2. **Superposition Theorem:** This theorem states that in a linear circuit with multiple independent sources, the voltage across (or current through) an element is the algebraic sum of the voltages (or currents) caused by each independent source acting alone, with all other independent sources turned off (replaced by their internal resistances). 3. **Steps to Solve:** - Identify all independent sources in the circuit. - For each source, turn off all other independent sources: replace voltage sources with short circuits and current sources with open circuits. - Calculate the voltage drop across the 2 ohm resistor due to each source acting alone. - Sum all these voltage drops algebraically to find the total voltage drop across the 2 ohm resistor. 4. **Formula:** $$V_{total} = V_1 + V_2 + \cdots + V_n$$ where $V_i$ is the voltage drop across the resistor due to the $i^{th}$ source alone. 5. **Example Calculation:** - Suppose the circuit has two voltage sources $V_a$ and $V_b$. - Calculate $V_{2\Omega, a}$ with $V_b$ turned off. - Calculate $V_{2\Omega, b}$ with $V_a$ turned off. - Then, $V_{2\Omega, total} = V_{2\Omega, a} + V_{2\Omega, b}$. 6. **Important Notes:** - Turning off a voltage source means replacing it with a wire (short circuit). - Turning off a current source means replacing it with an open circuit. - Ensure to keep track of polarity and direction when summing voltages. Without the specific circuit values or configuration, this is the general method to find the voltage drop across the 2 ohm resistor using superposition.