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The problem asks to determine the total resistance between points \(a\) and \(b\) in the given circuit. The circuit appears to be a combination of resistors in series and parallel. Here's how we can analyze it step by step:

### Step-by-Step Solution:

1. **Identify Parallel and Series Combinations**:
    - From the image, we see that the resistors are grouped into parallel and series.
    - The resistors \(12 \Omega\), \(26 \Omega\), and \(40 \Omega\) are in **parallel**.
    - The resistors \(60 \Omega\), \(30 \Omega\), and \(14 \Omega\) are also in **parallel**.
    - These two parallel combinations are then connected in **series**.

2. **Calculate Equivalent Resistance for the First Parallel Group** (12Ω, 26Ω, 40Ω):
   The formula for resistors in parallel is:
   \[
   \frac{1}{R_{\text{eq1}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
   \]
   Substituting the values:
   \[
   \frac{1}{R_{\text{eq1}}} = \frac{1}{12} + \frac{1}{26} + \frac{1}{40}
   \]
   Solving this gives \(R_{\text{eq1}}\).

3. **Calculate Equivalent Resistance for the Second Parallel Group** (60Ω, 30Ω, 14Ω):
   Using the same formula for parallel resistors:
   \[
   \frac{1}{R_{\text{eq2}}} = \frac{1}{60} + \frac{1}{30} + \frac{1}{14}
   \]
   Solving this gives \(R_{\text{eq2}}\).

4. **Add the Two Equivalent Resistances in Series**:
   Once we have \(R_{\text{eq1}}\) and \(R_{\text{eq2}}\), we can add them since they are in series:
   \[
   R_{\text{total}} = R_{\text{eq1}} + R_{\text{eq2}}
   \]

I will now calculate these values for you.The calculations yield the following results:

- The equivalent resistance of the first parallel group (12Ω, 26Ω, 40Ω) is approximately \(6.81 \, \Omega\).
- The equivalent resistance of the second parallel group (60Ω, 30Ω, 14Ω) is approximately \(8.24 \, \Omega\).
- Therefore, the total resistance between points \(a\) and \(b\) is the sum of these two, which is approximately \(15.05 \, \Omega\).

Let me know if you want any more details or explanations.

Here are some related questions to explore further:
1. What is the formula for calculating resistance in parallel and series circuits?
2. How does changing one resistor in a parallel circuit affect the overall resistance?
3. What are the practical applications of parallel and series resistances in real-world circuits?
4. How would adding an additional resistor in series to the current setup change the total resistance?
5. How can we verify the total resistance in a real circuit using multimeters?

**Tip**: Always double-check whether resistors are in series or parallel before applying formulas to ensure correct calculations.

Determine the total resistance at points a and b of the circuit shown below.

Find the total resistance between points a and b in a complex circuit involving both parallel and series resistors. This problem uses the formulas for series and parallel resistance to simplify and solve the circuit step by step, with the final resistance calculated as approximately 15.05 Ohms.

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