n resistors each of resistance R first combine to give maximum effective resistgance and then combine to give minimum. The ratio of the maximum resistance is

Options

A. n
B. `n^(2)`
C. `n^(2)-1`
D. `n^(3)`

Explanation

To solve the problem, we need to find the ratio of the maximum effective resistance to the minimum effective resistance when combining n resistors, each of resistance R.

### Step-by-Step Solution:

1. **Understanding Series and Parallel Combinations**:
- When resistors are combined in **series**, the effective resistance (R_max) is the sum of the individual resistances.
- When resistors are combined in **parallel**, the effective resistance (R_min) is given by the reciprocal of the sum of the reciprocals of the individual resistances.

2. **Calculating Maximum Resistance**:
- For n resistors connected in series:
\[ R_{\text{max}} = R + R + R + \ldots + R \quad (n \text{ times}) = nR \]

3. **Calculating Minimum Resistance**:
- For n resistors connected in parallel:
\[ \frac{1}{R_{\text{min}}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \ldots + \frac{1}{R} \quad (n \text{ times}) = \frac{n}{R} \]
- Therefore, the effective resistance is:
\[ R_{\text{min}} = \frac{R}{n} \]

4. **Finding the Ratio of Maximum to Minimum Resistance**:
- Now, we need to find the ratio of maximum resistance to minimum resistance:
\[ \text{Ratio} = \frac{R_{\text{max}}}{R_{\text{min}}} = \frac{nR}{\frac{R}{n}} \]
- Simplifying this expression:
\[ \text{Ratio} = \frac{nR \cdot n}{R} = n^2 \]

5. **Final Answer**:
- The ratio of the maximum effective resistance to the minimum effective resistance is:
\[ \text{Ratio} = n^2 \]