A piece of wire of resistance `R` is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is `R'`, then the ratio `R//R'` is :

Options

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

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Understand the resistance of each part after cutting the wire
The total resistance of the wire is given as \( R \). When the wire is cut into 5 equal parts, the resistance of each part can be calculated using the formula for resistance, which is proportional to the length of the wire.

The resistance of each part will be:
\[ R_{\text{part}} = \frac{R}{5} \]

### Step 2: Calculate the equivalent resistance when connected in parallel
When these 5 parts are connected in parallel, the formula for equivalent resistance \( R' \) for resistors in parallel is given by:
\[ \frac{1}{R'} = \frac{1}{R_{\text{part}}} + \frac{1}{R_{\text{part}}} + \frac{1}{R_{\text{part}}} + \frac{1}{R_{\text{part}}} + \frac{1}{R_{\text{part}}} \]

Substituting \( R_{\text{part}} = \frac{R}{5} \):
\[ \frac{1}{R'} = 5 \cdot \frac{1}{\frac{R}{5}} = 5 \cdot \frac{5}{R} = \frac{25}{R} \]

### Step 3: Solve for \( R' \)
To find \( R' \), we take the reciprocal of both sides:
\[ R' = \frac{R}{25} \]

### Step 4: Calculate the ratio \( \frac{R}{R'} \)
Now we can find the ratio \( \frac{R}{R'} \):
\[ \frac{R}{R'} = \frac{R}{\frac{R}{25}} = 25 \]

### Conclusion
Thus, the ratio \( \frac{R}{R'} \) is \( 25 \).