In a potentiometer wire, whose resistance in `0.5 ohm//m`, a current of 2 amp is passing. The value of potential grandient in volt/m will be

Options

A. `0.1`
B. `0.5`
C. `1.0`
D. 4

Explanation

To find the potential gradient in a potentiometer wire, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Resistance per Unit Length**:
The resistance of the potentiometer wire is given as \(0.5 \, \Omega/m\).

2. **Determine the Total Resistance**:
If we denote the length of the wire as \(L\) meters, then the total resistance \(R\) of the wire can be calculated as:
\[ R = 0.5 \, \Omega/m \times L = 0.5L \, \Omega \]

3. **Use Ohm's Law to Find Potential Difference**:
According to Ohm's law, the potential difference \(V\) across a resistor is given by:
\[ V = I \times R \]
where \(I\) is the current flowing through the wire. Given that the current \(I = 2 \, A\), we can substitute the values:
\[ V = 2 \, A \times 0.5L \, \Omega = 1L \, V \]

4. **Calculate the Potential Gradient**:
The potential gradient (PG) is defined as the potential difference per unit length:
\[ PG = \frac{V}{L} \]
Substituting the expression for \(V\):
\[ PG = \frac{1L \, V}{L} = 1 \, V/m \]

5. **Conclusion**:
Therefore, the value of the potential gradient in the potentiometer wire is:
\[ \text{Potential Gradient} = 1 \, V/m \]