How will you connect three resistors of `2Omega, 3Omega` and `5Omega` respectively so as to obtain a resultant resistance of `2.5 Omega`? Draw the diagram to show the arrangement.

Answer

To connect three resistors of 2Ω, 3Ω, and 5Ω to obtain a resultant resistance of 2.5Ω, we can follow these steps:

### Step 1: Understanding Series and Parallel Connections
- In a series connection, the total resistance (R_total) is the sum of the individual resistances:
\[ R_{\text{total}} = R_1 + R_2 + R_3 \]
- In a parallel connection, the total resistance (R_total) can be calculated using the formula:
\[ \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]

### Step 2: Connecting 2Ω and 3Ω in Series
- First, we connect the 2Ω and 3Ω resistors in series:
\[ R_{A} = 2Ω + 3Ω = 5Ω \]
- The equivalent resistance of this series connection (R_A) is 5Ω.

### Step 3: Connecting the Resultant Resistance in Parallel with 5Ω
- Now, we connect this resultant 5Ω resistance in parallel with the 5Ω resistor:
\[ \frac{1}{R_{\text{total}}} = \frac{1}{R_A} + \frac{1}{5Ω} \]
\[ \frac{1}{R_{\text{total}}} = \frac{1}{5Ω} + \frac{1}{5Ω} \]
\[ \frac{1}{R_{\text{total}}} = \frac{2}{5Ω} \]
\[ R_{\text{total}} = \frac{5Ω}{2} = 2.5Ω \]

### Step 4: Drawing the Circuit Diagram
- The circuit diagram will show the 2Ω and 3Ω resistors connected in series, and this combination connected in parallel with the 5Ω resistor.

### Final Arrangement
- The final arrangement is:
- 2Ω and 3Ω in series (resulting in 5Ω)
- This 5Ω in parallel with the 5Ω resistor

### Diagram
```
+---[2Ω]---[3Ω]---+
| |
| |
+--------[5Ω]-----+
```

### Summary
- By connecting the 2Ω and 3Ω resistors in series to form a 5Ω resistance and then connecting this 5Ω resistance in parallel with the other 5Ω resistor, we achieve a resultant resistance of 2.5Ω.