How to Apply Thevenin's Theorem and Calculate Load Voltage in Circuits

Hello! I'm excited to help you work through this Thevenin's theorem problem! This is a fundamental skill in circuit analysis that will make complex circuits much easier to handle.

What We're Solving:

We need to use Thevenin's theorem to simplify the circuit at terminals A-B, then calculate the load voltage for two different resistor values (600Ω and 1.8kΩ).

The Approach:

Thevenin's theorem is like having a "circuit simplification superpower"! It lets us replace any complex circuit (as seen from two terminals) with just two components: a voltage source (VTh) and a series resistor (RTh). This makes calculations SO much easier, especially when we need to analyze different load values.

Here's why this is brilliant: instead of re-analyzing the entire complex circuit each time we change the load, we just work with our simple Thevenin equivalent!

Step-by-Step Solution:

Step 1: Find the Thevenin Voltage (VTh)

• Remove the load resistor from terminals A-B
• Calculate the open-circuit voltage across terminals A-B
• This becomes our VTh (the voltage you'd measure with a voltmeter across A-B with no load)

Step 2: Find the Thevenin Resistance (RTh)

• Remove the load resistor AND turn off all independent sources:

- Replace voltage sources with short circuits (wire) - Replace current sources with open circuits

• Calculate the equivalent resistance looking into terminals A-B
• This becomes our RTh

Step 3: Draw the Thevenin Equivalent Circuit

• VTh in series with RTh, connected to terminals A-B
• Now you have a beautifully simple circuit!

Step 4: Calculate Load Voltages For any load resistor RL, use voltage division: VL = VTh × (RL)/(RTh + RL)

Note: I notice you haven't included the original circuit diagram. To give you specific numerical answers, I'd need to see the circuit values and configuration.

The Answer:

Without the specific circuit values, the general answers are:

• (i) For 600Ω load: VL = VTh × (600)/(RTh + 600)
• (ii) For 1.8kΩ load: VL = VTh × (1800)/(RTh + 1800)

Once you provide the circuit diagram, I can help you calculate the exact numerical values!

Memory Tip:

Remember Thevenin's theorem with this phrase: "Any circuit is just a battery and a resistor in disguise!"

The Thevenin voltage is what the circuit "wants" to output, and the Thevenin resistance is what "fights against" the current flow.

Would you like to share the circuit diagram so we can work through the specific numbers together? You're doing great tackling this important concept! 🌟