Instructions: Answer all questions. Marks are indicated against each question.

Passive Elements: Passive elements are electrical components that cannot generate power; they can only dissipate or store energy. They do not require an external power source to operate. The three fundamental passive elements are resistors, capacitors, and inductors.

1. Resistor (R): A resistor is a two-terminal electronic component that produces a voltage drop across it when the electric current flows through it. It opposes the flow of current. The relationship between voltage (V), current (I), and resistance (R) is described by Ohm's Law:

Resistors dissipate energy in the form of heat. They are used to control current, divide voltage, and provide a load.

2. Capacitor (C): A capacitor is a passive electronic component that stores electrical energy in an electric field. It consists of two conductive plates separated by an insulating dielectric material. A capacitor opposes changes in voltage across it. The current through a capacitor is proportional to the rate of change of voltage:
Capacitors store energy and are used in filtering, smoothing, and timing circuits.

3. Inductor (L): An inductor is a passive electronic component that stores energy in a magnetic field when electric current flows through it. It typically consists of a coil of wire. An inductor opposes changes in current flowing through it. The voltage across an inductor is proportional to the rate of change of current:
Inductors store energy and are used in filters, transformers, and oscillators.

Active Elements: Active elements are electrical components that can generate power or deliver energy to a circuit. They typically require an external power source to operate or can amplify a signal.

1. Voltage Source: A voltage source provides a constant voltage across its terminals, regardless of the current drawn from it (ideal voltage source). Real voltage sources have internal resistance. They supply energy to the circuit. Examples include batteries and power supplies.

2. Current Source: A current source provides a constant current, regardless of the voltage across its terminals (ideal current source). Real current sources have internal parallel resistance. They supply energy to the circuit.

3. Transistors: Transistors are semiconductor devices that can act as amplifiers or switches. They control a large current or voltage between two points in a circuit by applying a small voltage or current between another pair of points. They require a power supply to operate and can amplify signals, thus delivering more power than they receive from the control signal.

4. Operational Amplifiers (Op-Amps): Op-amps are high-gain electronic voltage amplifiers. They are versatile active components used in a wide range of analog circuits for amplification, filtering, signal conditioning, and more. They require dual power supplies to operate and can amplify input signals significantly.

In summary, passive elements consume or store energy, while active elements generate or deliver energy and can control power flow.

Objective: To find the current flowing through the 6Ω resistor using Thevenin's theorem.

Thevenin's Theorem: Thevenin's theorem states that any linear electrical network with respect to two terminals can be replaced by an equivalent circuit consisting of a single voltage source (V_th) in series with a single impedance (Z_th) or resistance (R_th).

Steps:

1. Find the Thevenin's equivalent voltage (V_th):
   - Remove the load resistor (6Ω in this case).
   - Calculate the open-circuit voltage across the terminals where the load was connected. This is V_th.
   - From the figure, the 6Ω resistor is connected across terminals A and B. We need to find the voltage V_AB when the 6Ω resistor is removed.
   - The circuit now consists of a 10V source, a 2Ω resistor, and a 4Ω resistor in series. The 6Ω resistor is removed.
   - The current flowing through the series combination of 2Ω and 4Ω resistors is:
   I = 10V / (2Ω + 4Ω) = 10V / 6Ω = 5/3 A
   
   - The voltage across the 4Ω resistor (which is V_AB or V_th) is:
   V_th = V_AB = I * 4Ω = (5/3 A) * 4Ω = 20/3 V ≈ 6.67 V
2. Find the Thevenin's equivalent resistance (R_th):
   - Deactivate all independent sources. Voltage sources are replaced by short circuits, and current sources are replaced by open circuits.
   - In this circuit, the 10V voltage source is replaced by a short circuit.
   - The equivalent resistance R_th is the resistance seen from terminals A and B.
   - The 2Ω resistor is now in parallel with the 4Ω resistor, as both are connected across the short-circuited voltage source terminals.
   - R_th = (2Ω || 4Ω) = (2 * 4) / (2 + 4) = 8 / 6 = 4/3 Ω ≈ 1.33 Ω
3. Construct the Thevenin's equivalent circuit:
   - The Thevenin's equivalent circuit consists of V_th in series with R_th, connected to the load resistor (6Ω).
4. Calculate the current in the 6Ω resistor:
   - The total resistance in the Thevenin's equivalent circuit is R_total = R_th + R_load = (4/3 Ω) + 6Ω = (4/3 + 18/3) Ω = 22/3 Ω.
   - The current flowing through the 6Ω resistor (I_load) is given by Ohm's Law:
   I_load = V_th / R_total = (20/3 V) / (22/3 Ω) = 20/22 A = 10/11 A
   
   - Therefore, the current in the 6Ω resistor is approximately 0.909 A.

Conclusion: Using Thevenin's theorem, the current flowing through the 6Ω resistor is 10/11 A.