The potential gradient of potentiometer is `0.2 "volt"//m`. A current of 0.1 amp is flowing throgh a coil of 2 ohm resistance. The balancing length in meters for the potential difference at the ends of this coil will be

Options

A. 2
B. 1
C. 0.2
D. 0.1

Explanation

To solve the problem, we need to find the balancing length for the potential difference across a coil with a given resistance and current flowing through it. Here’s how we can approach the solution step by step:

### Step 1: Understand the given data
- Potential gradient (V/m) = 0.2 V/m
- Current (I) = 0.1 A
- Resistance (R) = 2 Ω

### Step 2: Calculate the potential difference (V) across the coil using Ohm's Law
Ohm's Law states that:
\[ V = I \times R \]
Substituting the values:
\[ V = 0.1 \, \text{A} \times 2 \, \Omega = 0.2 \, \text{V} \]

### Step 3: Relate the potential difference to the balancing length
The potential gradient is defined as the potential difference per unit length. Therefore, we can express the potential difference in terms of the balancing length (L):
\[ \text{Potential Gradient} = \frac{V}{L} \]
Rearranging gives us:
\[ L = \frac{V}{\text{Potential Gradient}} \]

### Step 4: Substitute the values into the equation
Now we can substitute the values we have calculated:
\[ L = \frac{0.2 \, \text{V}}{0.2 \, \text{V/m}} \]

### Step 5: Calculate the balancing length
\[ L = 1 \, \text{m} \]

### Final Answer
The balancing length for the potential difference at the ends of the coil is **1 meter**.

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