Explain whole question---**Question 1:**
a) State and explain superposition theorem.
b) Find the current in the 7 $\Omega$ resistor across AB of the network using Superposition theorem:
**Circuit Diagram Description:**
* **Type:** Electrical circuit diagram.
* **Components:**
* One current source labeled "5 A" with an upward arrow.
* One voltage source labeled "1 V" with positive terminal on the right and negative terminal on the left.
* Five resistors:
* One 1 $\Omega$ resistor connected horizontally.
* One 1 $\Omega$ resistor connected vertically.
* One 1 $\Omega$ resistor connected diagonally from top-left to bottom-right, part of a bridge-like structure.
* One 1 $\Omega$ resistor connected diagonally from bottom-left to top-right, part of the bridge-like structure.
* One 7 $\Omega$ resistor connected vertically on the right side, labeled as being across points A and B.
* **Points:**
* Point A: Top end of the 7 $\Omega$ resistor.
* Point B: Bottom end of the 7 $\Omega$ resistor.
* **Connections:**
* The current source is connected between a common node (bottom line) and a node to the left of the horizontal 1 $\Omega$ resistor.
* The horizontal 1 $\Omega$ resistor connects the node from the current source to point A.
* The vertical 1 $\Omega$ resistor connects the common node to a node below point A and left of the voltage source.
* The two diagonal 1 $\Omega$ resistors are connected in a bridge configuration. The top-left 1 $\Omega$ resistor connects the node below point A and left of the voltage source to the node to the right of the voltage source. The bottom-left 1 $\Omega$ resistor connects the common node to the node to the right of the voltage source.
* The voltage source is connected between the node below point A and left of the voltage source (negative terminal) and the node to the right of the voltage source (positive terminal).
* The 7 $\Omega$ resistor is connected between point A and point B.
* Point B is connected to the node to the right of the voltage source and also to the common node.
* **Labels and Annotations:**
* Current source value: 5 A (arrow pointing upwards).
* Voltage source value: 1 V (positive terminal on the right).
* Resistor values: 1 $\Omega$ (four resistors), 7 $\Omega$ (one resistor).
* Points A and B.
* An arrow labeled "I'" is shown pointing downwards through the 7 $\Omega$ resistor, indicating the current direction to be found.
* **Relative Position:** The current source is on the left, the bridge structure with the voltage source is in the center, and the 7 $\Omega$ resistor is on the right between points A and B. The bottom line appears to be a common ground or reference node.
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The superposition theorem is a fundamental principle in linear circuit analysis. It states that in any linear bilateral network with multiple independent sources, the current through or voltage across any element equals the algebraic sum of the currents or voltages produced by each source acting independently. To apply this theorem, we consider one source at a time while replacing other voltage sources with short circuits and current sources with open circuits.
For Case 1, we consider only the 5 ampere current source. We replace the 1 volt voltage source with a short circuit. This creates a simplified circuit where the 5 ampere current flows through a series path consisting of the 1 ohm horizontal resistor and the 7 ohm resistor between points A and B. Since these resistors are in series with the current source, the current through the 7 ohm resistor equals the source current of 5 amperes, flowing downward from A to B.
For Case 2, we consider only the 1 volt voltage source. We replace the 5 ampere current source with an open circuit. This isolates Node 1, creating no current path to point A. Since point A becomes floating with no current entering or leaving it, the voltage at point A equals the reference voltage of 0 volts. Therefore, the current through the 7 ohm resistor is zero amperes. The contribution from the voltage source to the current in the 7 ohm resistor is zero.
Now we apply the superposition theorem by taking the algebraic sum of both contributions. From Case 1 with the current source, we found 5 amperes downward. From Case 2 with the voltage source, we found 0 amperes. The total current equals 5 amperes plus 0 amperes, which gives us 5 amperes flowing downward from point A to point B through the 7 ohm resistor. This is our final answer using the superposition theorem.
In summary, we successfully applied the superposition theorem to find the current in the 7 ohm resistor. We analyzed two cases separately: first considering only the 5 ampere current source which contributed 5 amperes downward, and second considering only the 1 volt voltage source which contributed zero amperes. The algebraic sum gives us the final answer of 5 amperes flowing downward from point A to point B. This demonstrates the power of superposition theorem in analyzing linear circuits with multiple independent sources.