R is the equivalent resistance of n resistors of same resistance in series. If the connection is turned parallel then equivalent resistance will be:

Options

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

Explanation

To find the equivalent resistance of \( n \) resistors of the same resistance \( R \) when connected in parallel, we can follow these steps:

### Step 1: Understand the Series Connection
When \( n \) resistors of resistance \( r \) are connected in series, the equivalent resistance \( R \) is given by:
\[ R = n \cdot r \]
This means that if you have \( n \) resistors, the total resistance is simply the sum of all individual resistances.

### Step 2: Find the Resistance of a Single Resistor
From the equation above, we can express the resistance of a single resistor \( r \) in terms of the equivalent resistance \( R \):
\[ r = \frac{R}{n} \]

### Step 3: Understand the Parallel Connection
When these \( n \) resistors are connected in parallel, the formula for equivalent resistance \( R_{eq} \) is given by:
\[ \frac{1}{R_{eq}} = \frac{1}{r} + \frac{1}{r} + \ldots + \frac{1}{r} \quad (n \text{ times}) \]
This simplifies to:
\[ \frac{1}{R_{eq}} = n \cdot \frac{1}{r} \]

### Step 4: Substitute the Value of \( r \)
Now, substituting \( r \) from Step 2 into the equation:
\[ \frac{1}{R_{eq}} = n \cdot \frac{1}{\frac{R}{n}} = n \cdot \frac{n}{R} = \frac{n^2}{R} \]

### Step 5: Solve for \( R_{eq} \)
Taking the reciprocal to find \( R_{eq} \):
\[ R_{eq} = \frac{R}{n^2} \]

### Conclusion
Thus, the equivalent resistance \( R_{eq} \) of \( n \) resistors of the same resistance \( R \) when connected in parallel is:
\[ R_{eq} = \frac{R}{n^2} \]