Thevenin's Theorem Explanation

Key Parameters

• Vth: Thevenin voltage across load terminals.
• Rth: Thevenin resistance seen from the load terminals.

Steps to Solve Using Thevenin's Theorem

1. Identify Load Resistance (RL):

   • Determine RL: In the example, RL is taken as R2.
   • Remove RL from the circuit to analyze the rest of the circuit.

2. Finding Vth:

   • After removing RL, identify points A and B (where RL was connected).
   • Calculate Vth as the voltage across A and B after RL is removed.
   • Use methods such as series/parallel calculations to find the voltage difference.
   • For current through the circuit:
     • Use the formula:
       [ I = \frac{V1 - V2}{R1 + R3} ]
   • Understand KVL (Kirchhoff’s Voltage Law) for voltage drops in the loop.

3. Finding Rth:

   • After finding Vth, determine Rth by looking into the circuit from the load terminals A and B, replacing all sources:
     • Replace voltage sources with short circuits.
   • Combine resistances R1 and R3:
     • Determine if they are in series or parallel based on circuit configuration.

4. Thevenin's Equivalent Circuit:

   • Draw the Thevenin equivalent circuit with Vth and Rth in series across the load terminals (AB).

5. Connect Load Resistance:

   • Connect the load resistance RL back across terminals A and B.
   • Use the formula to find the current through the load: [ I_L = \frac{V_{th}}{R_{th} + R_L} ]

Example Summary

• Remove Load: Identify and remove RL, taking careful note of the points A and B.
• Calculate Vth: Determine the voltage drop from A to B after removing RL, considering potential drops across R1 and R3. Use KVL for calculations.
• Calculate Rth: Find the equivalent resistance by replacing sources and simplifying the network.
• Final Circuit: After obtaining Vth and Rth, draw the Thevenin equivalent circuit, reconnect the load and calculate current.

Important Notes

• The analysis can vary based on the circuit; careful attention to series and parallel connections is essential.
• Always verify the direction of current and voltage drops when applying KVL.
• The general approach will always involve removing the load, finding the Thevenin parameters, and reconnecting to find desired values.