We have n resistors each of resistance R. The ratio of the combination for maximum and minimum values is

Options

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

Explanation

To find the ratio of the maximum and minimum resistance values when combining n resistors each of resistance R, we can follow these steps:

### Step 1: Calculate Maximum Resistance
The maximum resistance occurs when all resistors are connected in series. The formula for the equivalent resistance \( R_{eq} \) in series is:
\[ R_{eq} = R_1 + R_2 + R_3 + \ldots + R_n \]
Since each resistor has the same resistance \( R \):
\[ R_{eq} = R + R + R + \ldots + R \quad (n \text{ times}) = nR \]
Thus, the maximum resistance \( R_{max} \) is:
\[ R_{max} = nR \]

### Step 2: Calculate Minimum Resistance
The minimum resistance occurs when all resistors are connected in parallel. The formula for the equivalent resistance \( R_{eq} \) in parallel is:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots + \frac{1}{R_n} \]
Again, since each resistor has the same resistance \( R \):
\[ \frac{1}{R_{eq}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \ldots + \frac{1}{R} \quad (n \text{ times}) = \frac{n}{R} \]
Thus, the equivalent resistance \( R_{eq} \) is:
\[ R_{eq} = \frac{R}{n} \]
So, the minimum resistance \( R_{min} \) is:
\[ R_{min} = \frac{R}{n} \]

### Step 3: Calculate the Ratio of Maximum to Minimum Resistance
Now, we find the ratio of the maximum resistance to the minimum resistance:
\[ \text{Ratio} = \frac{R_{max}}{R_{min}} = \frac{nR}{\frac{R}{n}} = \frac{nR \cdot n}{R} = n^2 \]

### Final Answer
Thus, the ratio of the combination for maximum and minimum values is:
\[ \text{Ratio} = n^2 \]