The maximum resistance which can be made using four resistor each of resistance `(1)/(2) Omega ` is

Options

A. `2 Omega`
B. `1 Omega`
C. `2 . 5 Omega`
D. `8 Omega`

Explanation

To find the maximum resistance that can be made using four resistors, each with a resistance of \( \frac{1}{2} \, \Omega \), we will connect all the resistors in series. Here’s the step-by-step solution:

### Step 1: Understand the Configuration
To achieve maximum resistance, we need to connect the resistors in series. In a series connection, the total resistance is the sum of the individual resistances.

### Step 2: Identify the Resistance of Each Resistor
Each resistor has a resistance of \( \frac{1}{2} \, \Omega \).

### Step 3: Calculate the Total Resistance in Series
When resistors are connected in series, the total resistance \( R_{\text{total}} \) is given by the formula:
\[ R_{\text{total}} = R_1 + R_2 + R_3 + R_4 \]
Since all resistors have the same resistance \( R = \frac{1}{2} \, \Omega \), we can write:
\[ R_{\text{total}} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} \]

### Step 4: Simplify the Calculation
Now, we can simplify the addition:
\[ R_{\text{total}} = 4 \times \frac{1}{2} = 2 \, \Omega \]

### Step 5: Conclusion
Thus, the maximum resistance that can be obtained using four resistors of \( \frac{1}{2} \, \Omega \) each is:
\[ \boxed{2 \, \Omega} \]