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The circuit shown in the image has resistors arranged in a combination of series and parallel.

1. **Series combination of resistors**: When resistors are connected in series, the total (or equivalent) resistance is the sum of the resistances:
   \[
   R_{\text{series}} = R_1 + R_2
   \]

2. **Parallel combination of resistors**: When resistors are connected in parallel, the total (or equivalent) resistance is calculated using the formula:
   \[
   \frac{1}{R_{\text{parallel}}} = \frac{1}{R_{\text{series}}} + \frac{1}{R_3}
   \]
   Or equivalently:
   \[
   R_{\text{parallel}} = \frac{R_{\text{series}} \cdot R_3}{R_{\text{series}} + R_3}
   \]

### Step-by-Step Solution:

- Given:
  - \( R_1 = 43 \, \Omega \)
  - \( R_2 = 66 \, \Omega \)
  - \( R_3 = 63 \, \Omega \)

1. **Combine \( R_1 \) and \( R_2 \) in series**:
   \[
   R_{\text{series}} = R_1 + R_2 = 43 \, \Omega + 66 \, \Omega = 109 \, \Omega
   \]

2. **Combine the result with \( R_3 \) in parallel**:
   \[
   \frac{1}{R_{\text{eq}}} = \frac{1}{R_{\text{series}}} + \frac{1}{R_3} = \frac{1}{109 \, \Omega} + \frac{1}{63 \, \Omega}
   \]
   Simplifying this:
   \[
   \frac{1}{R_{\text{eq}}} = 0.009174 + 0.015873 = 0.025047
   \]
   Thus, the equivalent resistance is:
   \[
   R_{\text{eq}} = \frac{1}{0.025047} \approx 39.92 \, \Omega
   \]

   Rounding to two significant figures:
   \[
   R_{\text{eq}} \approx 40 \, \Omega
   \]

### Final Answer: \( R_{\text{eq}} = 40 \, \Omega \)

Would you like further details on this? Here are some related questions:

1. What is the difference between resistors in series and in parallel?
2. How would the equivalent resistance change if the value of \( R_3 \) were halved?
3. What would be the impact of increasing \( R_1 \) by 20% on the total resistance?
4. Can you explain the formula for resistors in parallel more intuitively?
5. How is energy dissipated in such a resistor network?

**Tip**: Always remember to check whether resistors are in series or parallel before calculating the equivalent resistance in a circuit.

Find the equivalent resistance between points A and B for the group of resistors shown in the figure. Suppose R1 = 43Ω, R2 = 66Ω, and R3 = 63Ω. Express your answer using two significant figures.

Learn how to find the equivalent resistance in a circuit involving a combination of resistors in series and parallel. This problem involves calculating the series resistance of R1 and R2, followed by combining it with R3 in parallel. Suitable for students studying physics at the high school or college level.

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