What is the minimum resistance the one can obtain by connecting all the five resistances each o f 1/5Ω

Options

A. `1/10 Omega`
B. `1/5 Omega`
C. `1/50Omega`
D. `1/25 Omega`

Explanation

To find the minimum resistance that can be obtained by connecting five resistors, each of \( \frac{1}{5} \, \Omega \), we can connect them in parallel. The formula for calculating the equivalent resistance \( R_{eq} \) when resistors are connected in parallel is given by:

\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} + \frac{1}{R_5} \]

### Step-by-Step Solution:

1. **Identify the resistance values**:
Each resistor has a resistance of \( R = \frac{1}{5} \, \Omega \).

2. **Set up the equation for parallel resistors**:
Since all five resistors have the same resistance, we can simplify the equation:
\[ \frac{1}{R_{eq}} = \frac{1}{\frac{1}{5}} + \frac{1}{\frac{1}{5}} + \frac{1}{\frac{1}{5}} + \frac{1}{\frac{1}{5}} + \frac{1}{\frac{1}{5}} \]

3. **Calculate the individual terms**:
Each term \( \frac{1}{\frac{1}{5}} = 5 \). Therefore, we have:
\[ \frac{1}{R_{eq}} = 5 + 5 + 5 + 5 + 5 = 25 \]

4. **Find the equivalent resistance**:
Now, we can find \( R_{eq} \) by taking the reciprocal of the sum:
\[ R_{eq} = \frac{1}{25} \, \Omega \]

5. **Conclusion**:
The minimum resistance that can be obtained by connecting all five resistors in parallel is:
\[ R_{eq} = \frac{1}{25} \, \Omega \]

### Final Answer:
The minimum resistance is \( \frac{1}{25} \, \Omega \).

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