How do you analyze circuits with dependent and independent sources using network theorems?

Superposition Theorem:

The Superposition Theorem is applicable to circuits with multiple independent sources (voltage or current) and linear components. To analyze the circuit using the Superposition Theorem, follow these steps:

Step 1: Turn off all independent sources except one.

Step 2: Analyze the circuit with only the active independent source (keeping the dependent sources as they are) using standard circuit analysis techniques (e.g., Ohm's Law, Kirchhoff's laws, nodal analysis, mesh analysis, etc.).

Step 3: Repeat steps 1 and 2 for each independent source, one at a time.

Step 4: Find the total response by adding up the individual responses from each independent source.

Keep in mind that when turning off an independent voltage source, it becomes a short circuit (replace it with a wire), and when turning off an independent current source, it becomes an open circuit (replace it with an open circuit).

Thevenin's Theorem:

Thevenin's Theorem is applicable to circuits with independent and dependent sources, but it requires the circuit to be linear. To analyze the circuit using Thevenin's Theorem, follow these steps:

Step 1: Identify the load or the part of the circuit you want to analyze.

Step 2: "Disconnect" the load by removing it from the original circuit.

Step 3: Calculate the Thevenin equivalent voltage (Vth) and Thevenin equivalent resistance (Rth) as seen from the load terminals. To find Vth, set all independent sources to zero (replace voltage sources with short circuits and current sources with open circuits) and find the voltage across the load terminals. To find Rth, deactivate all independent sources and find the equivalent resistance seen from the load terminals.

Step 4: Replace the original circuit with the Thevenin equivalent circuit, consisting of Vth in series with Rth.

Step 5: Analyze the load circuit using standard techniques, considering the Thevenin equivalent circuit.

It's essential to note that Thevenin's Theorem is only applicable to circuits with a linear response. If the circuit contains nonlinear elements, you may need to use other techniques, such as numerical methods or simulation software.

These network theorems provide a systematic approach to analyze circuits with both dependent and independent sources, making circuit analysis more manageable and efficient. However, always ensure you have a good understanding of the underlying principles of circuit theory to apply these theorems effectively.