The resistance of the wire is 121 ohm. It is divided into .n. equal parts and they are connected in parallel, then effective resistance is 1 ohm. The value of .n. is

Options

A. 12
B. 13
C. 11
D. 3

Answer

To solve the problem, we need to find the value of \( n \) given that the resistance of a wire is \( 121 \, \Omega \), and when divided into \( n \) equal parts connected in parallel, the effective resistance becomes \( 1 \, \Omega \).

### Step-by-Step Solution:

1. **Identify the Resistance of Each Part**:
The total resistance of the wire is \( R = 121 \, \Omega \). When the wire is divided into \( n \) equal parts, the resistance of each part \( R_i \) can be calculated as:
\[ R_i = \frac{R}{n} = \frac{121}{n} \, \Omega \]

2. **Use the Formula for Effective Resistance in Parallel**:
When resistors are connected in parallel, the formula for the effective resistance \( R_{eq} \) is given by:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots + \frac{1}{R_n} \]
Since all resistors are equal, we can simplify this to:
\[ \frac{1}{R_{eq}} = n \cdot \frac{1}{R_i} = n \cdot \frac{1}{\frac{121}{n}} = \frac{n}{121} \]

3. **Set Up the Equation for Effective Resistance**:
We know from the problem that the effective resistance \( R_{eq} = 1 \, \Omega \). Therefore, we can set up the equation:
\[ \frac{n}{121} = \frac{1}{R_{eq}} = 1 \]

4. **Solve for \( n \)**:
Rearranging the equation gives:
\[ n = 121 \]

5. **Conclusion**:
The value of \( n \) is \( 11 \).

### Final Answer:
The value of \( n \) is \( 11 \).