Resistance `n`, each of `r ohm`, when connected in parallel give an equivalent resistance of `R ohm`. If these resistances were connected series, the combination would have a resistance in ohm, equal to

Options

A. `n^(2) R`
B. `R // n^(2)`
C. `R // n`
D. nR

Explanation

To solve the problem, we need to find the equivalent resistance when `n` resistors, each of resistance `r ohm`, are connected in series, given that their equivalent resistance when connected in parallel is `R ohm`.

### Step-by-Step Solution:

1. **Understanding Parallel Resistance**:
The formula for the equivalent resistance \( R \) of \( n \) resistors each of resistance \( r \) connected in parallel is given by:
\[ \frac{1}{R} = \frac{1}{r} + \frac{1}{r} + \ldots + \frac{1}{r} \quad (n \text{ times}) \]
This can be simplified to:
\[ \frac{1}{R} = \frac{n}{r} \]
Therefore, we can express \( R \) as:
\[ R = \frac{r}{n} \]

2. **Finding Individual Resistance**:
From the equation above, we can rearrange it to find \( r \):
\[ r = nR \]

3. **Understanding Series Resistance**:
When the same \( n \) resistors are connected in series, the equivalent resistance \( R_{eq} \) is simply the sum of all individual resistances:
\[ R_{eq} = r + r + \ldots + r \quad (n \text{ times}) = n \times r \]

4. **Substituting the Value of \( r \)**:
Now, substituting the value of \( r \) from step 2 into the series resistance formula:
\[ R_{eq} = n \times (nR) = n^2 R \]

5. **Final Result**:
Thus, the equivalent resistance when the resistors are connected in series is:
\[ R_{eq} = n^2 R \]

### Conclusion:
The equivalent resistance when the resistors are connected in series is \( n^2 R \).