Let's break down the circuit and solve for the **equivalent resistance (\(R_{eq}\))** step by step. --- ## 1. **Identify the Configuration** Given values: - \(R_1 = 6\ \text{k}\Omega\) - \(R_2 = 3\ \text{k}\Omega\) - \(R_3 = 6\ \text{k}\Omega\) - \(R_4 = 6\ \text{k}\Omega\) From the diagram: - \(R_2\) and \(R_3\) are **in series**. - Their combination is **in parallel** with \(R_4\). - That whole section is **in series** with \(R_1\). --- ## 2. **Calculate Series Combination (\(R_2\) and \(R_3\))** \[ R_{23} = R_2 + R_3 = 3 + 6 = 9\ \text{k}\Omega \] --- ## 3. **Find Parallel Combination with \(R_4\)** Parallel resistors: \[ \frac{1}{R_{234}} = \frac{1}{R_{23}} + \frac{1}{R_4} \] \[ \frac{1}{R_{234}} = \frac{1}{9} + \frac{1}{6} \] Find a common denominator: \[ \frac{1}{9} + \frac{1}{6} = \frac{2}{18} + \frac{3}{18} = \frac{5}{18} \] \[ R_{234} = \frac{18}{5} = 3.6\ \text{k}\Omega \] --- ## 4. **Add \(R_1\) in Series** \[ R_{eq} = R_1 + R_{234} = 6 + 3.6 = 9.6\ \text{k}\Omega \] --- ## 5. **Conclusion** **The correct answer is \(9.60\ \text{k}\Omega\) (to 4 significant figures: 9.600).** --- ### **Where the Error Was** - The answer "1.714" is too low and likely due to a misunderstanding of the circuit configuration. - Always check the series and parallel combinations step by step. --- ### **Summary Table** | Step | Calculation | Result (\(\text{k}\Omega\)) | |-------------------------|---------------------------|-----------------------| | Series: \(R_2 + R_3\) | \(3 + 6\) | 9 | | Parallel: with \(R_4\) | \((9 \parallel 6)\) | 3.6 | | Series: add \(R_1\) | \(6 + 3.6\) | 9.6 | --- Let me know if you need more explanation or a drawing!

# Understanding the Circuit Let's analyze the circuit step by step to find the **equivalent resistance (\(R_{eq}\))**. ## 1. Circuit Configuration ### Given Values: - \(R_1 = 6\ \text{k}\Omega\) - \(R_2 = 3\ \text{k}\Omega\) - \(R_3 = 6\ \text{k}\Omega\) - \(R_4 = 6\ \text{k}\Omega\) ### Configuration: - **\(R_2\) and \(R_3\)** are in **series**. - The combination of \(R_2\) and \(R_3\) is in **parallel** with \(R_4\). - The entire configuration is in **series** with \(R_1\). ## 2. Calculate Series Combination ### Step 1: Combine \(R_2\) and \(R_3\) \[ R_{23} = R_2 + R_3 = 3 + 6 = 9\ \text{k}\Omega \] ## 3. Calculate Parallel Combination with \(R_4\) ### Step 2: Combine \(R_{23}\) and \(R_4\) \[ \frac{1}{R_{234}} = \frac{1}{R_{23}} + \frac{1}{R_4} \] \[ \frac{1}{R_{234}} = \frac{1}{9} + \frac{1}{6} \] ### Finding a Common Denominator: \[ \frac{1}{9} + \frac{1}{6} = \frac{2}{18} + \frac{3}{18} = \frac{5}{18} \] \[ R_{234} = \frac{18}{5} = 3.6\ \text{k}\Omega \] ## 4. Add \(R_1\) in Series ### Step 3: Final Calculation for \(R_{eq}\) \[ R_{eq} = R_1 + R_{234} = 6 + 3.6 = 9.6\ \text{k}\Omega \] ## 5. Conclusion **The equivalent resistance is \(9.60\ \text{k}\Omega\) (to 4 significant figures: 9.600).** ## Error Analysis The answer "1.714" appears to be incorrect, likely due to a misunderstanding of the series and parallel combinations. It's important to carefully analyze each step in the circuit configuration. ## Summary of Steps 1. **Combine Series \(R_2\) and \(R_3\)**: \(R_{23} = 9\ \text{k}\Omega\) 2. **Combine Parallel \(R_{23}\) and \(R_4\)**: \(R_{234} = 3.6\ \text{k}\Omega\) 3. **Add \(R_1\) in Series**: \(R_{eq} = 9.6\ \text{k}\Omega\) Feel free to ask if you need further clarification or assistance!