How do you analyze circuits with dependent and independent voltage/current sources?

Understand the Circuit:

Examine the circuit diagram and identify all the components, including resistors, capacitors, inductors, voltage sources, current sources, and dependent sources. Note their values or expressions, as well as their connections.

Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL):

Apply Kirchhoff's voltage law and Kirchhoff's current law to find equations that relate the voltages and currents in the circuit. These laws state that the sum of voltages around any closed loop in a circuit is zero (KVL) and the sum of currents at any node is zero (KCL).

Use Ohm's Law:

Apply Ohm's law (V = IR) to determine the relationship between voltage, current, and resistance for resistors in the circuit.

Solve for Unknowns:

Set up equations based on KVL, KCL, and Ohm's law to solve for the unknown voltages and currents in the circuit.

Dependent Sources:

For circuits with dependent sources (sources whose values depend on other voltages or currents in the circuit), use the relationships provided by the dependent sources to express these sources in terms of the unknown variables. Substitute these expressions into the circuit equations.

Simplify the Equations:

Simplify the circuit equations by eliminating unnecessary variables using the expressions obtained from dependent sources. This process may involve substitution and algebraic manipulation.

Apply Network Theorems (Optional):

In some cases, you can apply network theorems such as Thevenin's theorem, Norton's theorem, superposition theorem, or any other theorem that helps simplify the circuit or solve for specific variables.

Solve the Equations:

Solve the simplified circuit equations to find the unknown voltages and currents in the circuit.

Verify and Interpret Results:

After obtaining the solutions, double-check your work to ensure it aligns with the original circuit diagram and is physically meaningful. Interpret the results in the context of the circuit's behavior.

It's important to note that the complexity of the circuit and the types of sources present will determine the approach you take in analyzing it. Additionally, simulation software like SPICE or circuit simulators can be valuable tools for more complicated circuits. For advanced or complex circuits, you may need to use advanced techniques, such as nodal analysis or mesh analysis, to solve the system of equations.