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This is a circuit problem where the task is to find the equivalent resistance between points \( a \) and \( b \), and all resistances are \( 60 \ \Omega \).

### Steps to solve:

1. **Identify the circuit type:**
   The given circuit resembles a **Wye (Y) to Delta (Δ)** conversion problem. The middle resistor forms a central triangle that can be simplified using a Y-Δ or Δ-Y transformation.

2. **Simplify the central triangle:**
   The middle triangle consists of three \( 60 \ \Omega \) resistors. We can use the Δ-Y transformation formula to convert these into a simpler Y-network, or we could apply a series-parallel approach by inspecting symmetry.

3. **Delta-Wye conversion:**
   The resistance of each branch of the Y network can be computed using the Δ-to-Y transformation formulas:
   
   \[
   R_Y = \frac{R_{\Delta}}{3}
   \]
   Since each resistor in the Δ is \( 60 \ \Omega \), the equivalent resistance for each branch in Y is:
   
   \[
   R_Y = \frac{60 \times 60}{60 + 60 + 60} = 20 \ \Omega
   \]

4. **Re-drawing the circuit:**
   After the Δ-Y transformation, each leg of the Y network now has \( 20 \ \Omega \) resistances. This makes it easier to combine resistances in series and parallel as needed.

5. **Compute the total resistance:**
   After applying the Δ-Y transformation, the circuit will have several resistors in series and parallel, which can be calculated step by step.

Let me go through these calculations step-by-step and provide the exact equivalent resistance calculation.After applying the Δ-to-Y transformation, the equivalent resistance for each leg of the Y-network is \( 20 \ \Omega \).

Now, the circuit can be simplified with these \( 20 \ \Omega \) resistors. I'll proceed with combining the resistors in series and parallel to compute the total equivalent resistance between terminals \( a \) and \( b \).The equivalent resistance between terminals \( a \) and \( b \) is approximately \( 24 \ \Omega \).

Do you have any questions, or would you like further clarification on any step?

Here are five related questions you can explore:
1. How do you perform a Wye (Y) to Delta (Δ) transformation in general?
2. What is the significance of series and parallel resistor combinations?
3. How does symmetry in a circuit help simplify resistance calculations?
4. Can you calculate the equivalent resistance if resistors have different values?
5. How does adding more branches affect the overall resistance in parallel circuits?

**Tip:** When simplifying complex resistor networks, always look for symmetry and try to reduce the circuit step by step using series-parallel combinations or transformations like Δ-Y.

Calculate the equivalent resistance between a and b terminals. All of the resistances are 60 Ω.

This problem focuses on calculating the equivalent resistance between two terminals of a resistor network where each resistor is 60 Ω. Learn how to simplify the circuit using Delta-Wye transformations and apply series-parallel combinations. Suitable for high school students learning advanced physics or electronics.

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