(1) Find the voltage drop across the 3 Ohm resistor by using super position theorem
The Correct Answer and Explanation is :
The Superposition Theorem is a fundamental principle in circuit analysis that simplifies the evaluation of circuits with multiple independent sources. It states that in a linear circuit with more than one independent source, the voltage or current in any component is equal to the algebraic sum of the voltages or currents produced by each source acting alone, with all other sources replaced by their internal impedances. citeturn0search1
Applying the Superposition Theorem to Find the Voltage Drop Across a 3-Ohm Resistor:
- **Identify the Independent Sources:**
- Determine all independent voltage and current sources present in the circuit.
- **Analyze the Circuit with One Source Active:**
- Deactivate all other sources:
- Replace all other voltage sources with short circuits (i.e., replace them with a wire).
- Replace all other current sources with open circuits (i.e., remove them).
- Calculate the current through and voltage across the 3-ohm resistor due to the active source.
- Deactivate all other sources:
- **Repeat for Each Source:**
- Reactivate the next source and repeat the deactivation and analysis steps for all other sources.
- **Sum the Individual Effects:**
- Add the individual voltage drops across the 3-ohm resistor from each analysis to find the total voltage drop.
Example:
Consider a circuit with two independent sources: a 10V voltage source and a 2A current source, both connected in series with a 3-ohm resistor.
- **Step 1: Analyze with the 10V Voltage Source Active:**
- Deactivate the 2A current source by replacing it with an open circuit.
- The current through the 3-ohm resistor is I=10V3Ω=3.33AI = \frac{10V}{3\Omega} = 3.33A.
- The voltage drop across the 3-ohm resistor is V=I×R=3.33A×3Ω=10VV = I \times R = 3.33A \times 3\Omega = 10V.
- **Step 2: Analyze with the 2A Current Source Active:**
- Deactivate the 10V voltage source by replacing it with a short circuit.
- The current through the 3-ohm resistor is 2A.
- The voltage drop across the 3-ohm resistor is V=I×R=2A×3Ω=6VV = I \times R = 2A \times 3\Omega = 6V.
- **Step 3: Sum the Effects:**
- The total voltage drop across the 3-ohm resistor is 10V+6V=16V10V + 6V = 16V.
By applying the Superposition Theorem, we have determined that the voltage drop across the 3-ohm resistor is 16V when both sources are active.
Limitations of the Superposition Theorem:
- It is applicable only to linear circuits, where components like resistors, inductors, and capacitors exhibit linear relationships between voltage and current.
- It cannot be used to calculate power directly, as power is a nonlinear function of voltage and current.
- It is not applicable to circuits with dependent sources or non-linear components like diodes and transistors.
Understanding and applying the Superposition Theorem is essential for simplifying complex circuit analyses, especially when dealing with multiple independent sources.