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To calculate the equivalent resistance between nodes \( A \) and \( C \), we can proceed by analyzing the circuit. The resistors form a combination of series and parallel connections. Let's work through this step-by-step:

### Step 1: Analyze the circuit structure

- \( R_1 \) and \( R_2 \) are in series between \( A \) and \( B \).
- \( R_3 \) is directly between nodes \( B \) and \( C \).
- \( R_4 \) is between nodes \( D \) and \( C \), and \( R_5 \) connects \( B \) to \( D \).

We need to find the equivalent resistance between \( A \) and \( C \).

### Step 2: Combine resistors in series and parallel

1. **Parallel between \( R_2 \) and \( R_5 \):**
   - Since \( R_2 \) and \( R_5 \) are in parallel between \( B \) and \( D \):
   \[
   R_{25} = \frac{R_2 \times R_5}{R_2 + R_5} = \frac{89.2 \times 29.3}{89.2 + 29.3}
   \]

2. **Combine \( R_1 \) (in series with \( R_{25} \))**:
   - The combined resistance between \( A \) and \( D \):
   \[
   R_{A-D} = R_1 + R_{25}
   \]

3. **Combine the parallel combination of \( R_3 \) and \( R_4 \) (between \( B \), \( C \), and \( D \)):**
   - Since \( R_3 \) and \( R_4 \) are in parallel between \( B \) and \( C \):
   \[
   R_{34} = \frac{R_3 \times R_4}{R_3 + R_4}
   \]

4. **Calculate the total equivalent resistance between \( A \) and \( C \):**
   - The equivalent resistance is the sum of \( R_{A-D} \) and \( R_{34} \):
   \[
   R_{eq} = R_{A-D} + R_{34}
   \]

Let me compute these values step by step.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, if you'd like, I can guide you through the remaining calculations manually or you can try the computation later using the formulae provided. Do you need further clarification or help with the process?

Here are some follow-up questions that might help expand your understanding:

1. What happens when two resistors are in parallel compared to when they are in series?
2. How does Kirchhoff's circuit law apply to this particular circuit?
3. Can you explain the significance of the equivalent resistance between two nodes in a circuit?
4. How would the result change if one of the resistors were replaced with a short circuit?
5. What tools or methods could be used to measure these resistances in a real-world circuit?

**Tip:** For circuits with resistors in both parallel and series, break them down step by step, starting with the simplest resistor combinations first.

Calculate the equivalent resistance between nodes A and C in the circuit with resistors R1 = 19.7 ohms, R2 = 89.2 ohms, R3 = 38.2 ohms, R4 = 40.4 ohms, and R5 = 29.3 ohms.

Learn how to calculate the equivalent resistance between nodes A and C in a circuit with multiple resistors connected in series and parallel. This detailed solution covers key electrical concepts and formulas, suitable for high school physics students.

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