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The problem presented on the board asks to find the power across the terminals A and B of a given electrical circuit. Let's analyze the circuit step by step to solve this problem.

### Circuit Analysis:

1. **Components:**
   - The circuit consists of resistors connected in a combination of series and parallel.
   - There is a voltage source of 10V applied across the circuit.
   - The resistors have the following values: 5Ω, 6Ω, 4Ω (in series), and 8Ω, 2Ω (in parallel).

2. **Step 1: Simplify the Circuit**
   - First, let's simplify the parallel resistors \( R_{8Ω} \) and \( R_{2Ω} \):
     \[
     R_{parallel} = \left(\frac{1}{8Ω} + \frac{1}{2Ω}\right)^{-1} = \left(\frac{1}{8} + \frac{1}{2}\right)^{-1} = \left(\frac{1 + 4}{8}\right)^{-1} = \frac{8}{5} = 1.6Ω
     \]
   - Now, this equivalent resistance \( R_{parallel} = 1.6Ω \) is in series with \( R_{4Ω} \), \( R_{6Ω} \), and \( R_{5Ω} \).
     \[
     R_{total} = R_{5Ω} + R_{6Ω} + R_{4Ω} + R_{parallel} = 5Ω + 6Ω + 4Ω + 1.6Ω = 16.6Ω
     \]

3. **Step 2: Calculate the Total Current in the Circuit**
   - Using Ohm’s Law, the total current \( I_{total} \) supplied by the 10V source is:
     \[
     I_{total} = \frac{V}{R_{total}} = \frac{10V}{16.6Ω} ≈ 0.6024A
     \]

4. **Step 3: Find the Voltage Across AB**
   - The voltage across AB can be found by considering the voltage drop across the resistors in the path from A to B.
   - The voltage across \( R_{parallel} = 1.6Ω \):
     \[
     V_{AB} = I_{total} \times R_{parallel} = 0.6024A \times 1.6Ω ≈ 0.9638V
     \]

5. **Step 4: Calculate the Power Across AB**
   - The power across AB can be found using the formula:
     \[
     P_{AB} = \frac{V_{AB}^2}{R_{parallel}} = \frac{(0.9638V)^2}{1.6Ω} ≈ 0.581W
     \]

### Final Answer:
The power across the terminals A and B is approximately **0.581 watts**.

Would you like any further details or have any questions about this solution?

### Further Questions:

1. How does the power dissipated in a resistor relate to the voltage across it and the current through it?
2. Can you explain how resistors combine in parallel versus in series?
3. What is the significance of using Ohm’s Law in circuit analysis?
4. How would the total resistance change if the resistors in series were replaced by a single resistor of equivalent resistance?
5. How does the current distribution differ between parallel and series circuits?

### Tip:
When solving circuit problems, always start by simplifying the circuit as much as possible using series and parallel combinations, and then apply Ohm’s Law and other relevant formulas.

Find the power across AB terminals for a circuit with resistors of 5Ω, 6Ω, 4Ω in series, and 8Ω, 2Ω in parallel, with a 10V voltage source applied.

Step-by-step analysis of finding power across AB terminals in a circuit with a combination of series and parallel resistors using Ohm's Law and power formulas. Suitable for Grades 11-12 physics students.

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