What is the minimum resistance which can be made using five resistors each of `(1//5) Omega` ?

Options

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

Explanation

To find the minimum resistance that can be achieved using five resistors, each with a resistance of \( \frac{1}{5} \, \Omega \), we will connect them in parallel. Here’s the step-by-step solution:

### Step 1: Understand the Configuration
To achieve the minimum resistance, we need to connect the resistors in parallel. When resistors are connected in parallel, the total or equivalent resistance decreases.

### Step 2: Use the Formula for Parallel Resistance
The formula for the equivalent resistance \( R_{eq} \) of \( n \) resistors connected in parallel, each with resistance \( R \), is given by:
\[ R_{eq} = \frac{R}{n} \]
where \( R \) is the resistance of one resistor and \( n \) is the number of resistors.

### Step 3: Substitute the Values
In this case, each resistor has a resistance of \( R = \frac{1}{5} \, \Omega \) and we have \( n = 5 \) resistors.
\[ R_{eq} = \frac{\frac{1}{5}}{5} \]

### Step 4: Simplify the Expression
Now, simplify the expression:
\[ R_{eq} = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25} \, \Omega \]

### Step 5: Conclusion
Thus, the minimum resistance that can be achieved using five resistors of \( \frac{1}{5} \, \Omega \) each is:
\[ R_{eq} = \frac{1}{25} \, \Omega \]

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

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