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To find the Thévenin equivalent resistance \( R_{th} \) of the circuit to the left of \( R_L \), follow these steps:

### Step 1: Remove \( R_L \)
Since we are calculating the Thévenin resistance, we temporarily remove \( R_L \) from the circuit. This isolates the network to the left of \( R_L \), so we can determine the equivalent resistance of that part of the circuit.

### Step 2: Deactivate the Voltage Source
Replace the 3V voltage source with a short circuit (effectively making it a wire), because in Thévenin resistance calculations, we deactivate all independent sources. 

### Step 3: Identify Resistor Combinations
Now, analyze the resistor network with the voltage source shorted:

1. The 20 \(\Omega\) and 30 \(\Omega\) resistors at the top are in series:
   \[
   R_{top} = 20 \Omega + 30 \Omega = 50 \Omega
   \]

2. The 20 \(\Omega\) and 30 \(\Omega\) resistors at the bottom are also in series:
   \[
   R_{bottom} = 20 \Omega + 30 \Omega = 50 \Omega
   \]

3. Now, \( R_{top} \), \( R_{bottom} \), and the 50 \(\Omega\) resistor in the middle are all in parallel. The equivalent resistance \( R_{th} \) is found using the parallel resistance formula:
   \[
   \frac{1}{R_{th}} = \frac{1}{R_{top}} + \frac{1}{50 \Omega} + \frac{1}{R_{bottom}}
   \]
   Substituting the values:
   \[
   \frac{1}{R_{th}} = \frac{1}{50 \Omega} + \frac{1}{50 \Omega} + \frac{1}{50 \Omega} = \frac{3}{50 \Omega}
   \]
   \[
   R_{th} = \frac{50 \Omega}{3} \approx 16.67 \Omega
   \]

### Final Answer
The Thévenin equivalent resistance \( R_{th} \) is approximately:
\[
R_{th} \approx 16.67 \Omega
\]

Would you like further explanation on any part of the calculation?

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**Further Questions to Explore:**
1. How would you find the Thévenin equivalent voltage across the terminals of \( R_L \)?
2. How does removing \( R_L \) affect the calculation of the Thévenin equivalent?
3. What changes if we have a current source instead of a voltage source?
4. Why do we deactivate independent sources when calculating Thévenin resistance?
5. How would you find the Norton equivalent resistance from this circuit?

**Tip:** In circuits with multiple resistors, simplify by combining series and parallel resistors step-by-step.

What is the Thévenin equivalent resistance of the circuit to the left of the resistor RL in the circuit below? Give your answer in ohms [Ω].

Learn how to calculate the Thévenin equivalent resistance of a circuit with multiple resistors. This problem involves using series and parallel resistance calculations, suitable for college-level electrical engineering or physics students.

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