A wire of resistance `R` is divided in 10 equal parts. These parts are connected in parallel, the equivalent resistance of such connection will be

Options

A. `0.01 R`
B. `0.1 R`
C. `10 R`
D. `100 R`

Explanation

To solve the problem, we need to find the equivalent resistance when a wire of resistance \( R \) is divided into 10 equal parts and connected in parallel. Here’s a step-by-step solution:

### Step 1: Determine the resistance of each part
When the wire of resistance \( R \) is divided into 10 equal parts, the resistance of each part \( r \) is given by:
\[ r = \frac{R}{10} \]

### Step 2: Use the formula for equivalent resistance in parallel
When resistors are connected in parallel, the formula for the equivalent resistance \( R_{eq} \) is:
\[ \frac{1}{R_{eq}} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3} + \ldots + \frac{1}{r_n} \]
Since all parts have the same resistance \( r \), we can simplify this to:
\[ \frac{1}{R_{eq}} = \frac{1}{r} + \frac{1}{r} + \frac{1}{r} + \frac{1}{r} + \frac{1}{r} + \frac{1}{r} + \frac{1}{r} + \frac{1}{r} + \frac{1}{r} + \frac{1}{r} \]
This can be expressed as:
\[ \frac{1}{R_{eq}} = 10 \cdot \frac{1}{r} \]

### Step 3: Substitute the value of \( r \)
Substituting \( r = \frac{R}{10} \) into the equation:
\[ \frac{1}{R_{eq}} = 10 \cdot \frac{1}{\frac{R}{10}} = 10 \cdot \frac{10}{R} = \frac{100}{R} \]

### Step 4: Calculate the equivalent resistance
Now, taking the reciprocal to find \( R_{eq} \):
\[ R_{eq} = \frac{R}{100} \]

### Final Answer
Thus, the equivalent resistance of the 10 parts connected in parallel is:
\[ R_{eq} = \frac{R}{100} \quad \text{or} \quad 0.01R \]

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