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`

Answer

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

### Step-by-Step Solution:

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

2. **Finding the Value of `r`**:
From the equation \( R = \frac{r}{n} \), we can rearrange it to find \( r \):
\[ r = R \cdot n \]

3. **Understanding Series Resistance**:
When the same `n` resistors are connected in series, the equivalent resistance \( R_s \) is given by:
\[ R_s = r + r + r + \ldots + r \quad (n \text{ times}) \]
This simplifies to:
\[ R_s = n \cdot r \]

4. **Substituting the Value of `r`**:
Now, we substitute the value of \( r \) we found earlier:
\[ R_s = n \cdot (R \cdot n) = n^2 \cdot R \]

5. **Final Result**:
Thus, the equivalent resistance when `n` resistors of resistance `r` are connected in series is:
\[ R_s = n^2 R \]

### Final Answer:
The equivalent resistance when `n` resistors of `r ohm` each are connected in series is \( n^2 R \).