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To solve the problem of finding the equivalent resistance across terminals \( A \) and \( B \) using the star-delta conversion method, let's follow these steps:

### Step 1: Identifying the Delta Network
The delta network is formed by the resistors \(6 \, \Omega\), \(4 \, \Omega\), and \(8 \, \Omega\) connected between the nodes of the circuit.

We can label the points involved in the delta network as follows:
- \(A\) (top node),
- The center node where \( 6 \, \Omega\), \(4 \, \Omega \), and \(8 \, \Omega \) meet can be referred to as the internal node (labeled as node 1).

### Step 2: Applying Star-Delta Conversion
In star-delta conversion, the formula for converting a delta to a star network is as follows for each leg of the star:
\[
R_{\text{star}} = \frac{R_1 \cdot R_2}{R_{\text{sum}}}
\]
where \(R_1\), \(R_2\), and \(R_3\) are the resistances of the delta network, and \(R_{\text{sum}} = R_1 + R_2 + R_3\).

For the given resistances \(6 \, \Omega\), \(4 \, \Omega\), and \(8 \, \Omega\):
- Resistor between \(A\) and the center node (\(6 \, \Omega\)),
- Resistor between center node and terminal \(B\) (\(4 \, \Omega\)),
- Resistor between \(A\) and \(B\) (\(8 \, \Omega\)).

We will now convert this into a star configuration.

Let me calculate that for you.The resistances after converting the delta network into a star configuration are as follows:

- \( R_{\text{star A}} = 1.33 \, \Omega \) (between node \(A\) and the center),
- \( R_{\text{star B}} = 1.78 \, \Omega \) (between node \(B\) and the center),
- \( R_{\text{center}} = 2.67 \, \Omega \) (between the internal star node and the center).

### Step 3: Simplifying the Circuit
Now, after the conversion, the circuit will have the following configuration:

- The \(1.33 \, \Omega\) resistor connected from node \(A\) to the center,
- The \(1.78 \, \Omega\) resistor connected from node \(B\) to the center,
- The \(2.67 \, \Omega\) resistor between \(A\) and \(B\),
- Resistors \(5 \, \Omega\) and \(5 \, \Omega\) as they are already present.

Now, I'll calculate the equivalent resistance of the combined network.

Let me handle that computation for you next.### Step 4: Combine the Resistors

1. **Resistors in parallel:**
   - The \(5 \, \Omega\) resistor (left side) is in parallel with the combination of the star resistances:
     - \(1.33 \, \Omega\) (star) in series with the \(3 \, \Omega\) resistor, and 
     - The combination of resistances \(1.78 \, \Omega\) (star) and \(4 \, \Omega\) (parallel combination).

I'll now calculate the equivalent resistance for each section and the final total equivalent resistance across terminals \( A \) and \( B \).It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you would like to proceed manually, I can guide you through the steps to calculate the final equivalent resistance, or you can ask additional questions about this problem.

Here are five questions related to this:

1. How is the star-delta conversion applied to simplify circuits?
2. What is the formula to calculate the equivalent resistance for resistors in parallel?
3. How do you calculate equivalent resistance for resistors in series?
4. What are the conditions for using the star-delta transformation?
5. How does star-delta conversion impact complex circuit analysis?

**Tip:** Always simplify parallel and series resistor networks step-by-step to avoid confusion during calculations!

Calculate equivalent resistance across the terminals A and B of the circuit as shown in Fig. 2 using star-delta conversion.

Learn how to calculate the equivalent resistance across terminals A and B in a complex resistor network using the star-delta conversion method. This step-by-step guide includes the conversion formulas, series, and parallel resistor rules, suitable for electrical engineering students.

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